At the end of 2021, the Russian Ministry of Foreign Affairs published the draft of a treaty between Russia and NATO members that, among other things, would have required the latter to commit not to enlarge the Alliance further. The US agreed to discuss some of the issues raised in the draft, but made it clear that NATO’s open door policy was not up for debate. A few weeks later, citing the threat that NATO expansion allegedly posed to Russia as one of the main justifications for his decision, Putin announced that Russia would officially recognize the separatist republics in Donbas and shortly after ordered a full-scale invasion of Ukraine. From that moment on, the view that NATO expansion may actually have played a role in Putin’s decision to invade Ukraine became verboten and, except for a handful of people like John Mearsheimer (who has been widely reviled for it), almost everyone started parroting that NATO expansion had “nothing to do” with it.

It’s understandable that people don’t want to give the impression they are conceding something to Russian propaganda, but the fact that Russia’s invasion of Ukraine is wrong doesn’t mean that people in the Kremlin don’t actually see NATO expansion as a security threat and it didn’t play a role in their calculus. I think it clearly did, albeit in a more complicated way than people on both sides of this debate assume, though I don’t plan on making the case for that view in this article. Instead, I just want to discuss one specific argument against that view, because it has been particularly influential and illustrates how Russia scholars often tell only half the story in that debate.

The argument in question was made by Michael McFaul, a prominent scholar of post-communist Russia and the US Ambassador to Russia between 2012 and 2014, in a paper he co-authored with Robert Person, another Russia specialist. They acknowledge that since the end of the Cold War, NATO expansion has always been a source of tension between the US and Russia, but claim that Russia’s concerns over it have not been constant and that Putin in particular was pretty relaxed about the issue during his first years in power. In support of that argument, they quote several statements made by Putin during the period in question, in which he seemed to regard NATO expansion with equanimity. For instance, in a November 2001 interview, he declared:

Russia acknowledges the role of NATO in the world of today, Russia is prepared to expand its cooperation with this organization. And if we change the quality of the relationship, if we change the format of the relationship between Russia and NATO, then I think NATO enlargement will cease to be an issue — will no longer be a relevant issue.

McFaul and Person also point out that, when asked in the same interview whether he opposed the admission of the Baltic republics into NATO, Putin stated that Russia “cannot forbid people to make certain choices if they want to increase the security of their nations in a particular way”. They also note that a few months later he said during a press conference with Ukrainian president Leonid Kuchma that he expected Ukraine to develop closer ties with NATO and that in any case “the decision [was] to be taken by NATO and Ukraine”. They infer from these statements that Putin “is not genuinely frightened by” NATO expansion and that we must look elsewhere for the source of his hostility towards Ukraine and the West. They argue that what Putin really fears is not the expansion of NATO but that of democracy and that he “fabricated this crisis about NATO expansion to undermine Ukrainian democracy”.

The problem with this narrative is that McFaul and Person omit crucial context about those statements that totally undermines the conclusion they draw from them. First, while the statements they quote make it sound as if Putin had no problem with NATO expansion, he made it very clear even at the time that he thought it was a bad idea. For instance, in the same November 2001 interview they quote, Putin also said that he didn’t think that expanding NATO “[made] any sense” because NATO had been created to deal with the threat posed by the Soviet Union and “there [was] no Soviet Union anymore”, so NATO expansion wouldn’t increase anyone’s security. Similarly, during a press conference in 2004 with Jaap de Hoop Scheffer, then Secretary General of NATO, he stated that “Russia's position toward the enlargement of NATO is well known and has not changed” and repeated his view that it wouldn’t increase anyone’s security, but strangely those statements and many others like them didn’t make it into McFaul and Person’s article.

Nevertheless, this raises the question of why, if Putin already saw NATO expansion as a threat at the time, he made the conciliatory statements towards the Alliance that McFaul and Person did quote. In order to answer that question, it’s necessary to explain the context in which they were made. At the time, NATO had just gone through its first post-Cold War round of expansion, which the Russians had opposed in the harshest terms before grudgingly accepting it because they didn’t have a choice. US officials were determined that NATO expansion would go ahead whether or not the Russians liked it, but they also wanted to preserve the relationship with Moscow if possible, so in parallel to the expansion process they started negotiations with Russia on a mechanism for cooperation with NATO that resulted in the signing of the NATO-Russia Founding Act in 1997. In particular, this agreement created the NATO-Russia Permanent Joint Council (PJC), in which consultation was supposed to take place on various issues identified as promising avenues for cooperation.

While officially this was presented as a transformation of the relationship between NATO and Russia, in reality it was mostly a face-saving exercise for Yeltsin’s benefit that would allow him to claim as a win what was really a concrete manifestation of Russia’s weakened state and loss of influence. As McFaul himself recounted in a book on US policy toward Russia he co-authored with James Goldgeier, after his advisers explained to him what the NATO-Russia Founding Act was, even Clinton wasn’t exactly impressed by what the US was offering Russia:

So let me get this straight. What the Russians get out of this great deal we’re offering them is a chance to sit in the same room with NATO and join us whenever we all agree to something, but they don’t have any ability to stop us from doing something that they don’t agree with. They can register their disapproval by walking out of the room. And for their second big benefit, they get our promise that we’re not going to put our military stuff into their former allies who are now going to be our allies, unless we happen to wake up one morning and decide to change our mind?

As McFaul and Goldgeier put it, Russia was “getting symbols rather than substance”, but it still took the deal because the US “did not need Russia in order to bring Poland into NATO” and even symbols are better than nothing.

Putin learned the lesson of that episode and, when he became president of Russia, decided to adopt a completely different strategy to deal with NATO expansion. He understood that opposing it head-on was not only pointless but even counterproductive. Russian officials had spent years denouncing it with at times hysterical rhetoric, but this had only exposed Russia’s weakness after the US went ahead with NATO expansion anyway and had arguably sped up the process by appearing to vindicate those who defended the policy on the ground that it was necessary as insurance against a resurgence of Russian imperialism. Since there was no point in opposing something that Russia couldn’t stop, Putin figured that it was better to go along with it in the hope that by adopting a cooperative stance he could obtain a transformation of the relationship with NATO that, unlike the NATO-Russia Founding Act, would not be limited to symbols but actually be substantive.

Indeed, what most people miss in this debate is that it’s not so much NATO expansion per se that Russia opposed as much as the exclusion of Moscow from the post-Cold War European security architecture that it entailed, because the Alliance, despite what the Russians had been led to believe at the end of the Cold War (but that’s a story for another time), had become the cornerstone of that architecture. If NATO became a more political organization and a mechanism could be found to include Russia in the decision-making process, then it would have no reason to fear NATO expansion. In fact, this is exactly what Putin was alluding to in the statement quoted by McFaul and Person, in which he said that if the “quality of the relationship” with NATO changed then enlargement would cease to be an issue. But you wouldn’t know that from reading their paper, because although they are perfectly aware of it, they carefully omit this context.

For a while, especially after Putin went out of his way to support the US in the aftermath of 9/11 and stuck with his decision to realign Russia with the West despite Bush’s decision to unilaterally withdraw from the Anti-Ballistic Missile Treaty (but that’s also a story for another time), it looked as if this strategy was actually working. In 2002, the NATO-Russia Council (NRC) was established, which replaced the PJC and promised a qualitative change in the nature of the relationship. Whereas in the PJC, Russia faced NATO as a bloc (the so-called “19 + 1” format), deliberations in the NRC would take place “at 20” and be based on the principle of equality, though NATO members still reserved the right to remove an issue from the NRC and discuss it without Russia if a consensus could not be reached at 20. Here is how George Robertson, then Secretary General of NATO, described this new framework during a press conference in November 2001:

[The new mechanism for cooperation] would involve Russia having an equality with the NATO countries in terms of the subject matter and would be part of the same compromising trade-offs, give and take, that is involved in day-to-day NATO business. That is how we do business at 19. The great United States of America, the mighty France and Germany, the United Kingdom have an equal voice to tiny Luxembourg and even tinier Iceland. But we get compromises. We build consensus. [So] the idea would be that Russia would enter that. That would give Russia a right of equality but also a responsibility and an obligation that would come from being part of the consensus-building organization.

Robertson pointed out that “a new attitude [was] going to be required on both sides if this [was] going to work”, but also noted that if it did, it would change “the way in which we do business”.

As we have seen, McFaul and Person quoted a statement that Putin made in 2002 during a press conference with Kuchma to the effect that he was fine with closer ties between NATO and Ukraine, but what they neglected to say is that he made this statement immediately after describing this new framework for cooperation between NATO and Russia:

Russia, as you know, is engaged in a very constructive dialogue with NATO to create a new Russia-NATO structure “at twenty”, in which all twenty countries will be represented as nations, each having one vote, and all the issues will be solved without prior consultations, without any prior decisions on a number of issues being taken first within the bloc.

Thus, it’s clear that if he made that statement at the time, it was because he thought that his strategy had worked and expected that NATO’s relationship with Russia was going to be transformed by the NRC. Indeed, the NRC promised to grant Russia some limited but nevertheless real decision-making power in concert with the Alliance, which would have gone some way towards alleviating Russia’s concerns about its exclusion from the post-Cold War European security architecture. As long as Russia had a say in decisions made by NATO, it wouldn’t have to worry if NATO continued to expand and became the cornerstone of that architecture, because it would have institutional means to make its voice heard from within and ensure that its interests were taken into account by the Alliance.

Of course, that was assuming that NATO kept up its part of the bargain, which it didn’t. Here is how Thomas Graham, who served as Associate Director of the Policy Planning Staff of the Department of State, then Director for Russian Affairs at the National Security Council and finally Special Assistant to the President during that period, described what happened:

The problem was that from the very beginning, the United States and the Bush administration weren’t prepared to deal with this Council as a meeting of 20 individual countries dealing on a national basis. What we did and what we insisted on is that NATO would get together before each meeting of the NATO-Russia Council in what we called the North Atlantic Council — the primary decision-making body of the NATO alliance — and in that meeting we would agree on what the common NATO position would be on the issue that we were going to discuss in the NATO-Russia Council. So … you didn’t have 20 countries sitting at the table, you had NATO in which 19 NATO members were obliged to present and pursue and support a certain approach to a problem, and a Russian approach that may or may not differ from the NATO approach. Again it didn’t take the Russians long to figure out what was going on, so I think that made the Council less attractive to them. And my argument always was that we ought to try at least one issue where we don’t have the NATO alliance agree beforehand what its unified position is going to be and see how the Russians conduct themselves and see what impact it has on alliance unity. And if it worked out well, then we could continue down this process. If it turned out bad, because we had predominant influence at that point because of our power, we could always find an off-ramp with very little loss to our ultimate position vis-à-vis the Russians and vis-à-vis our allies.

However, Graham wasn’t able to convince the rest of the administration and the US never gave the new mechanism a chance, even though NATO had promised the Russians that deliberations in the NRC would really take place “at 20” and not at “19 + 1”. Thus, while it continued to meet until the invasion of Ukraine in 2022 and arguably resulted in productive cooperation on some low-level issues, the NRC never transformed the NATO-Russia relationship in the way Putin hoped and had been promised.

Obviously, once you know the context of the statements quoted by McFaul and Person in their paper, they take on a very different meaning. If Putin made so many conciliatory statements on NATO expansion in the first years of his presidency, it’s not because he didn’t see it as a security threat if it implied Russia’s exclusion from the post-Cold War European security architecture, but because he thought that by adopting a cooperative stance on the issue Russia would be included in the decision-making process. For a while, it seemed that his strategy had paid off as NATO promised a new framework for cooperation that would have gone some way toward realizing this ambition, but in the end it didn’t happen because the US didn’t hold up its part of the bargain. Of course, McFaul and Person know about this, but they omit this context even though it undermines the simplistic narrative they are promoting. Nor is this episode the only legitimate grievance that Russia has toward the West, but as Russia scholar Marlène Laruelle recently noted, people are no longer interested in nuance when it comes to the degradation of relations between the two sides:

For me, the war is Putin’s responsibility, but the strategic deadlock that preceded it has been co-created by Russia and the West, with misunderstanding on both sides, and responsibilities on both sides. Whenever you try to bring in some nuance, then you get the accusation of being on Putin's side.

Unfortunately, she is right about that, which is a huge problem for the public discourse about the origins of the war.

In particular, the notion that NATO expansion has “nothing to do” with it has become a dogma that nobody can question in polite company, yet it’s not only false but preposterous. There are hundreds of memoirs, cables, memos, etc. spanning decades attesting that Russian elites have been genuinely frightened by the expansion of NATO. Nor is it the case, as people sometimes claim when you point that out, that if Russian officials have feared NATO expansion it’s only because it prevents Moscow from dominating its neighbors. I’m not saying that neo-imperialist considerations play no role, which would also be ridiculous, but Russian elites actually think that NATO expansion threatens Russia’s security. Now, I agree that their fears are to a large extent irrational (though not entirely), but Russian officials are not the first policymakers to have exaggerated security concerns, and nor will they be the last.

It’s ironic that many people who 20 years ago were convinced that Iraq posed such an imminent threat to the US that it had to be taken out immediately can’t even fathom the possibility that Russian elites might have a similarly inflated perception of the threat posed by NATO expansion. The notion that Putin just made this up and that Russian officials don’t really see NATO expansion as a security threat is so ridiculous that, if the public discourse about Russia were even minimally based in reality, nobody could make such a claim without suffering a serious reputational cost. However, as things are, it’s people who point that out whose reputations suffer because they’re accused of laundering Russian propaganda. Russia scholars bear a large responsibility for this state of affairs, because most of them know things are more complicated than what the dominant narrative claims, but they don’t speak up or even pretend that is not the case because they don’t want to pay the cost. While at some level their behavior is understandable, because in the current environment it’s very difficult to speak up against that narrative, I still think it’s a dereliction of duty.

Now, as I said at the beginning of this article, the way in which NATO expansion played a role in the origins of the war is more complicated than people on both sides commonly assume. In particular, it’s not so much that it was the proximate cause of the war, but rather that it contributed towards creating the conditions that made the war possible. The story of how this happened is complicated and Russia obviously has a huge share of responsibility in the degradations of relations with the West prior to the invasion, but it’s impossible to understand this process without acknowledging that Moscow has legitimate grievances against the West, as the episode I discussed in this article illustrates. The problem is that not only are those grievances never discussed, but when the Russians bring them up they are accused of making things up, which just adds insult to injury. If you were previously unaware of the history presented in this article, I hope that it has convinced you that things are more complicated than you thought.

Soon, I will publish the first part of a larger project on the history of post-Cold War relations between Russia, the West and Ukraine, in which I will give my interpretation of this complicated story. Understanding what led to the war and avoiding simplistic narratives is not only important because truth is intrinsically valuable, but also because it could help bring the conflict to a faster conclusion. Indeed, sooner or later, Russia and Ukraine will have to negotiate a settlement and, one way or another, Western countries will have to be part of the process. However, if people in the West are convinced that all the fault lies with Russia, it will be harder politically for Western governments to play a positive role in the negotiations, because this will necessarily require making compromises and making compromises is harder when you think that you don’t have any responsibility for the situation that people are trying to resolve. Moreover, if Westerners don’t understand what Russia wants and what it fears, it will be harder to make the difficult choices that will result in the best possible deal for everyone.

POST SCRIPTUM: I slightly edited the text of the article and the title, which initially accused McFaul of “lies of omission”, because he reached out to me and convinced me that it was counterproductive. To be clear, in using that expression, I was only referring to the fact that he failed to discuss the context of Putin’s statements. I never meant to suggest that, when he claims that Putin doesn't really fear NATO expansion and that it’s not why he invaded Ukraine, he is misrepresenting his actual view and that he doesn’t really believe that. In fact, I have no doubt that he does, but this just means that we have a different interpretation of the historical record. This is a perfectly legitimate scholarly disagreement and I should have kept it professional, so I apologize for using this kind of rhetoric. Obviously, this doesn’t change anything I said about the substantive issue, but how you say something is also important. The public debate about this is just very frustrating to me because I think it lacks nuance and every time someone tries to introduce some people accuse them of complicity with Putin, but as McFaul pointed out to me, he has his own reasons to be frustrated by the debate and I shouldn’t have let this get the better of me.

As Russian forces left the region of Kiev, large parts of which they had been occupying since the beginning of the invasion of Ukraine, atrocities were reported in several towns around the capital. The most shocking reports came from Bucha, a town with a pre-war population of 37,000 located about 15 miles north-west of Kiev, where many residents were apparently killed. Several pictures and videos of streets littered with corpses — some of them with their hands tied behind their back — have been posted on social media and the town’s mayor told the AFP that 280 people had been buried in mass graves. Russia has denied that it was responsible for those atrocities, claiming that pictures and videos of dead people were “staged” and arguing that Russian forces couldn’t have been responsible. In this post, I examine Russia’s argument, which I find unconvincing. I conclude that Russia almost certainly committed war crimes in Bucha, but that the extent of those crimes is not clear yet and that a thorough international investigation is called for to determine that and clearly establish who is responsible.

Russia’s argument that its forces are not responsible

The Russian Ministry of Defense published a post on Telegram in which it argued that Russian soldiers couldn’t have killed the people found in Bucha. The argument rests primarily on a comparison between the timeline of the Russian occupation of Bucha and that of the reports of atrocities:

We would like to emphasise that all Russian units withdrew completely from Bucha as early as March 30, the day after the Russia-Ukraine face-to-face round of talks in Turkey.

Moreover, on March 31, the mayor of Bucha, Anatoliy Fedoruk, confirmed in a video message that there were no Russian servicemen in the town, but he did not even mention any locals shot in the streets with their hands tied.

It is not surprising, therefore, that all the so-called “evidence of crimes” in Bucha did not emerge until the fourth day, when the Security Service of Ukraine and representatives of Ukrainian media arrived in the town.

Thus, Russia claims that its forces had completely withdrawn by March 30 and that even the mayor of Bucha confirmed on March 31 that Russian troops were gone, yet he didn’t mention any killings of civilians and the pictures and videos of corpses in the streets did not emerge until April 3.

Another argument that Russia made in that post is that the bodies shown in the pictures and videos published on social media are not in a state compatible with a death that occurred during the town’s occupation by the Russian forces:

It is of particular worry that all the bodies of the people whose images have been published by the Kiev regime are not stiffened after at least four days, have no typical cadaver stains, and the wounds contain unconsumed blood.

The implication of both of those arguments is that, if civilians were killed in Bucha, it couldn’t have been during the Russian occupation and they must therefore have been killed by someone else, but the statement actually goes further and concludes that the pictures and videos of dead civilians in Bucha are “staged” and the whole thing is a “hoax”.

Russia’s timeline is wrong and the evidence is consistent with the hypothesis that Russian forces killed civilians in Bucha

I have to admit that when I read the argument about the statement by the mayor of Bucha, I was troubled by it, so I decided to look into it and this quickly convinced me that Russia’s argument didn’t hold water. It’s true that the mayor published a video on Facebook in which he called March 31 “the day of Bucha’s liberation” and didn’t mention any bodies in the streets. However, contrary to what Russia claims, this video was posted not on March 31 but on April 1 at 6:31 pm local time. As far as I can tell, the first video of corpses in the streets of Bucha was published on Telegram the same day at 6:42 pm and, in the next few hours, several other pictures and videos of similar atrocities were published on social media.1 In other words, while it’s true that the mayor of Bucha didn’t mention any corpses in the streets in his statement, pictures and videos showing bodies in the streets of Bucha emerged almost immediately after he posted that statement. It would still be weird if Bucha had been liberated on March 31, as the mayor claimed in his statement, yet he didn’t mention the corpses littering the streets in a video he published on April 1, but a closer look at the evidence shows that’s not really what happened.

Indeed, another city official had posted a video on Bucha’s official Facebook page that morning at 10:18 am local time in which he claimed that the city was still occupied, urged residents to be cautious and even mentioned corpses in the streets. Thus, according to that post, liberation was still in progress during the morning of April 1. My guess is that Ukrainian forces started entering the town on March 31, which is why the mayor called it “the day of Bucha’s liberation”, but either there were still Russians at this point or the Ukrainians were not sure yet they were completely gone and didn’t confirm it until April 1.2 If the Ukrainian forces were still in the process of reoccupying the city on the morning of April 1 and people were not even sure that the Russians were completely gone at that time, it’s not particularly surprising that videos of the massacre didn’t emerge until later that day. It probably means that people were not summarily executed in every part of town, or at least that most of the corpses were brought to just some areas, but this is entirely consistent with the hypothesis that the Russian forces are responsible.

The other argument put forward by Russia is not particularly convincing either, but in that case I think a forensic investigation would be necessary to fully debunk it. Russia claims that, since its forces left Bucha on March 30 but photos and videos of corpses in the streets didn’t emerge until 4 days later, the bodies should have been stiff and more decomposed than they appeared. However, as we have seen, this timeline is wrong since, while it’s not entirely clear when the last Russian forces left Bucha exactly, the pictures and videos were first shared on the evening of April 1 and not on April 3 as Russia falsely claims. Furthermore, those pictures and videos don’t really allow us to judge the state of the bodies since they are dressed in warm clothes (let alone how stiff they were), so I find this argument totally unconvincing and don’t understand why anyone would take it seriously. Several Russian officials have also claimed that the videos coming out of Bucha are fake because the bodies of people supposed to be dead can be seen moving, but it has been shown that this was just because of low-quality video encoding.

Besides, The New York Times compared satellite pictures taken on March 19 with videos of bodies in a street of Bucha that were published on April 1 and found that the former showed the same number of bodies in the same positions as the latter, which implies that, even if we accept Russia’s claim that its forces left the town on March 30, several people whose bodies were later found in the streets were killed before that. I checked the temperature in Bucha between March 19 and April 1 on World Weather Online and found it was above freezing for most of that period, so I expect that the bodies must have been in a pretty bad state under the clothing, but only forensic examinations will be able to establish whether the state of the bodies is consistent with the timeline implied by the satellite pictures given the weather during that period.3 Forensic examinations will also be necessary to check whether the nature of the wounds on the bodies is compatible with the hypothesis that those people were killed by Russian forces, since even if they were killed during the occupation, they could have been killed by Ukrainian shelling of the town. However, in at least one case, we have a video taken by a drone showing Russian forces firing on a cyclist, whose body can be seen in photos and videos published after Bucha’s liberation.

Conclusion

I think at this point it’s virtually certain that Russian forces committed war crimes in Bucha. Not only are Russia’s arguments that its forces couldn’t have killed the people shown in pictures and videos shared on social media totally unconvincing, but since the town was liberated and images of atrocities emerged, many witnesses have testified that Russian soldiers had killed civilians in cold blood. Those testimonies seem credible to me, they are consistent with the evidence and, whatever you think of Ukrainian forces (who have also committed war crimes), I doubt they would have threatened local residents to force them to produce false testimonies incriminating Russian forces.4 Some people argue that it doesn’t make sense for Russian forces to commit such gruesome crimes right next to Kiev and leave the evidence behind in the streets as they leave, but the My Lai massacre also made no sense and it still happened. Unfortunately, it’s not uncommon for foreign armies to commit atrocities against civilians, especially when losses and frustration mount.

In my opinion, the real uncertainty is about the extent of the war crimes that Russian forces committed in Bucha, not whether they committed any. As we have seen, the mayor initially claimed that 280 people had been found in mass graves, but as far as I can tell no journalist has been able to confirm that and it’s possible that the real death toll is lower than that. For instance, journalists from The Washington Post only saw 58 body bags lined up in the town’s cemetery, although what some officials told them implies a much higher death toll. On the other hand, the mayor’s deputy told Reuters on April 5 that while 300 dead people had been found after the Russian forces left, only 50 of them had been confirmed to have been the result of executions so far. So I think that we still don’t know exactly how many people were executed by the Russian forces in Bucha. For this and other reasons, I think an international investigation is needed to establish exactly who did what in Bucha, but again the conclusion that Russia committed war crimes over there seems beyond much doubt at this point.

If you follow European politics even a little bit, you must have heard of Éric Zemmour, the former right-wing pundit who is running for president in France and who is now a serious contender for the second round of the election. Everyone thought the results of the April 2022 election were written in advance, with a second round between Macron and Le Pen, which the former would have won easily. But Zemmour's entry into the race and his rise in the polls suddenly made this campaign very interesting. Unless he collapses in the coming month, which I doubt, you're probably going to hear a lot more about him soon, so I figured that it might be useful to write a short post explaining who he is and what he wants and give some context that people not familiar with French politics might lack. I'm going to briefly present his background, platform, strengths and weaknesses and explain what his victory would entail and to what extent the comparisons people make with Trump are sensible. In the conclusion I will explain why his election would be a political earthquake in Europe.

Who is Éric Zemmour?

Éric Zemmour was born in 1958 to Jewish parents who had recently moved to France from Algeria, still a French colony at the time, but were French citizens since most Jews in Algeria had been granted citizenship in 1870. He was born in Montreuil near Paris, a city that is home to a large share of African and North-African immigrants, but despite what I often hear he is not himself an immigrant since he was born in France to French parents. However, it's true that he is not of European descent, so he is not a "Français de souche". He became a journalist in the 1980s and started covering national politics in 1996 for Le Figaro, France's main right-wing newspaper. Thus, over the years, he has met most French politicians and became friends with many of them. Most of them were conservative politicians, but not all of them. For instance, he is friends with Jean-Luc Mélenchon, the French far-left politician who even came to his birthday party a few years ago. During his career as a political journalist, he wrote biographies of Édouard Balladur and Jacques Chirac (the two most prominent right-wing politicians at the time), which although not bestsellers were favorably reviewed. Although he was well-known in political circles, the public did not discover him until the 2000s, when he became a regular on several TV shows and quickly became very popular for his abrasive style.

Although ideologically they are very different, during this period, he was a kind of Christopher Hitchens. He was no longer just a political journalist, but also and even mainly a cultural critic. In 2006, he wrote a book against the feminization of society — under the title The First Sex in reference to Simone de Beauvoir's famous book — which became a bestseller and horrified a lot of feminists. In that work, he explicitly defended the patriarchal model, something that was very controversial even in France and would be unimaginable in the US. He wrote several other bestsellers after that in which he revisited French history and denounced France's decline. He was fired several times from the TV shows and radio stations where he worked (where his left-wing colleagues signed petitions against him and pressured the bosses to get rid of him), but since he was very good for ratings, he would immediately be hired somewhere else. In 2011, he was found guilty of "incitement to racial hatred" by a court for saying that Blacks and Arabs were stopped by the police more often because "most [drug] traffickers are Black or Arab" (which is probably true), but this didn't do anything to make him less popular. He was convicted again in 2018 for "incitement toward religious hatred" against Muslims.

What's his platform?

According to various accounts, Zemmour started considering a political career a few years ago, before finally crossing the Rubicon a few months ago. Indeed, while he only made a formal announcement that he was running on November 30, he started preparing his campaign in the spring. The main theme of his campaign, overshadowing everything else, is the fight against immigration. He explicitly presents his bid for the presidency as the only way to prevent the Grand Remplacement ("Great Replacement"). According to him, unless France radically restricts immigration from North and sub-Saharan Africa (he says that we should aim for zero), people of non-European descent will eventually become the majority and the country will cease to be French culturally. While the first part is undoubtedly true and, in my opinion, the second is also correct, no French politician except Jean-Marie Le Pen had dared to say that before and it didn't have the same impact with him because he was totally radioactive. Even Marine Le Pen refused to use that expression because she was trying to make her party respectable and she thought it was too radical. While the idea of the "Great Replacement" make the sophisticates want to scream bloody murder, polls show that 2/3 of the French population think it's true, so it's not as if this idea is really controversial outside of the bubble in which most commentators live, but Zemmour managed to make it a major theme of the campaign, which is unprecedented.

It's not really surprising that Zemmour should run against the "Great Replacement", since he's been consistently anti-immigration and denouncing it for years in very strong terms. Indeed, as we have seen, it landed him in courts and caused him to lose his jobs on several occasions. Unlike many conservative politicians in both Europe and the US, Zemmour doesn't merely use anti-immigration rhetoric because it's popular among voters, he is a true believer. However, although he opposes immigration and despite what many people say, he doesn't have a racial conception of Frenchness, which indeed would be rather weird since he is of non-European descent. He thinks that anyone can be French, no matter their background, but that being French involves adopting French culture and not just having French citizenship. He often criticizes people who claim that, in order to be French, one just has to adhere to human rights and a few other abstract principles. But while he thinks that anyone can in theory be French, he believes that France, which has been unable to assimilate the non-European immigrants who are already here, won't be able to do so — let alone assimilate newcomers — if we don't stop immigration. Therefore, he doesn't attack only illegal immigration, but also and even mainly legal immigration. This includes asylum, which he wants to reduce to a few hundred people a year at most, citing Japan as his model because it only accepted 47 refugees in 2020.

Apart from immigration, Zemmour is a traditional conservative on most issues, but unlike most conservative politicians — who are far more liberal than their voters and say a lot of things they don't really mean to get their votes when they're running for office — there can be no doubt that he truly believes what he says, because he was already saying the same things before he decided to run for president. He is openly and stridently anti-woke, wants to remove what he calls "LGBT ideology" from schools and return to traditional pedagogy, increase the number of places in prison and the severity of sentences, etc. While in the past he has expressed somewhat heterodox views on economics, he is running on a very traditional French right-wing platform, pro-capitalism without being libertarian. His views on foreign policy are more original. He is openly a proponent of realpolitik and says that France should talk to everyone, including China and Russia. He is very critical of people who argue that we shouldn't negotiate with them because they violate human rights. Again, there is no doubt that he sincerely believes that, because this is something he's been saying for years. He also said that he thinks NATO should have been dismantled after the USSR collapsed, but has only proposed that France leave the organization's integrated command, not that it leave NATO altogether.

Is he the French Trump?

Many people compare Zemmour to Trump, both in the US and in France, which I think is right in some ways but misleading in others. There are certainly similarities between Zemmour and Trump. First, neither of them is a career politician and they both have used their media popularity as a launchpad for their political career. This makes sense, since unless you already have some name recognition, it's extremely difficult to make a dent in the polls when you don't have a political machine behind. They also have a similar communication strategy, consisting of being ubiquitous in the media, which is easy because although journalists are very hostile to them they are very good for ratings so they still cover them. They make politically incorrect statements that make the sophisticates clutch their pearls and for days that's all everyone hears about, which of course is exactly what they want, but journalists can't help it so it works every time. Another similarity is that, like Trump and unlike so many conservative politicians, Zemmour never backs down. When he says something that journalists consider outrageous, he doesn't apologize but doubles down, something that contributes a lot to his popularity among right-wing voters who are used to seeing conservative politicians grovel in front of the media every time they inadvertently say something that goes against the dominant opinion and also played a large role in Trump's success in 2016 according to me. However, Zemmour has a similar problem with women as Trump, something he'll have to solve if he is to have a chance:

Finally, while French presidential campaigns are much cheaper than in the US (expenditures are capped at 22 million euros by law), you still need money to have a chance and, like Trump in 2016, I have it on good authority that he is getting a lot of small donations, so I don't think money will be a problem despite what some people think.

However, despite those similarities, Zemmour is also very different from Trump in a number of ways. First, whereas Trump is a clown who has neither the taste nor the discipline to read a lot about the issues, Zemmour is a voracious reader and works hard to make up for his deficiencies in some domains such as economics. Trump had some ideological preferences, such as his opposition to immigration and foreign wars motivated by ideology, but he wasn't an ideologue and he spent his term in office hiring people who thought exactly the opposite as him, because in the end he didn't care much about the issues and personal relationships were much more important to him. In that respect, Zemmour is a completely different animal; he has deep ideological commitments and is highly unlikely to appoint anyone who isn't fully on board with his program. The socio-economic profile of their supporters is also different and reflects this difference in their personalities. Whereas Trump did particularly well among non-college educated voters, socio-economic category doesn't seem very predictive of voting intentions for Zemmour. This is also strikingly different from Le Pen and Macron, who do much better among non-college educated and college-educated voters, respectively. Similarly, age is not very predictive of voting intentions for Zemmour, whereas Le Pen does significantly better among prime age people and Macron overperforms among older people:

This difference between Trump and Zemmour in who they appeal to is also reflected in the profile of the people advising them. Intelligent people have tended to stay as far away from Trump as possible, so his advisers tended to be very stupid people, but Zemmour has attracted a lot of talent. Most people don't know them, because they mostly work in the shadows, but Zemmour is surrounded by a lot of people with a very unusual background for a candidate regarded as far-right. They tend to be young and come from the most prestigious schools in France. There are engineers, public servants, people in business, etc. Those profiles are very different from the crackpots Trump tended to surround himself with or, for that matter, from the people who advise Le Pen.

What is his strategy and does he have a chance?

Zemmour has been very explicit about his strategy, so we don't really have to guess, but in order to understand it you need to know a few things about French political history. Up until the 1980's, the French socialist party was a working-class movement. François Mitterrand, the first socialist to become president in France, was elected in 1981 on a platform that included the nationalization of many branches of industry. He actually implemented this platform after his election, but it was a disaster and he soon had to choose between his socialist economic policy and European integration, because continuing with this policy would have required that France leave the European Monetary System. In 1983, he chose the latter, but this decision created a serious political problem for him. Indeed, if the socialist party was no longer socialist on the economy, it needed something to mobilize voters against the right. The solution was to pivot from a party that was focused on improving the material conditions of the working class to a party that was focused on social issues and, in particular, on defending immigrants, who gradually replaced the working class in left-wing mythology. (Of course, I'm not saying it wouldn't have happened otherwise since left-wing parties in other Western countries underwent the same transformation, but it was particularly sharp in France.) Luckily for Mitterrand, at the same time, the National Front, Jean-Marie Le Pen's far-right party, was beginning to rise and its leader was the perfect bogeyman for the socialist party and its new platform.

At first, traditional right-wing leaders did not consider the National Front to be toxic and even made alliances with it occasionally in local elections, but as it turned out Mitterrand was really smart and traditional right-wing leaders were really stupid. Mitterrand very intelligently used his influence to simultaneously give more visibility to Le Pen by getting him invited on national television and also demonize him by supporting various anti-racist activist groups to make him a pariah by pretending that he was a fascist. Thus, while the National Front was rising and taking votes away from traditional right-wing parties, it was becoming increasingly difficult for them to make alliances because mainstream conservative politicians were afraid of the backlash from the media. Le Pen himself made that easier by making several very controversial statements and soon he was completely toxic. This gradually resulted in a division of the French right, with moderates and the conservative bourgeoisie voting mostly for traditional right-wing parties, while the National Front got more radical voters and, increasingly, working-class voters moving away from the communist party. Despite what many people in the US think, France is actually a deeply right-wing country in many ways, so the total vote in favor of the right is almost always greater than the total for the left, but this division of the right and the "cordon sanitaire" around the National Front nevertheless allowed the socialist party to sometimes win national election because the right couldn't unite.

This coup was a case of political genius on the part of Mitterrand and, for the past 30 years, it has plagued the French right and made it lose elections that it would otherwise have easily won. While this division of the right-wing electorate was initially pretty superficial, it eventually solidified because, to a large extent, people's ideology is driven by their partisan identity and not the other way around. Thus, the more time went by, the more difficult it became for the right to escape Mitterrand's curse by uniting. Nicolas Sarkozy understood this and his solution was to steal Le Pen's voters by adopting his platform while avoiding his excesses. Thus, he was able to unite the right without allying with the National Front, which allowed him to win the presidential election easily in 2007. But he quickly betrayed his promises and, under Marine Le Pen, the National Front — which recently became the National Rally — rose even higher than it had under her father. However, despite her efforts, it's still toxic enough that she can't possibly win the presidential election. Zemmour's theory is that he can unite the right around him by bringing together the conservative bourgeoisie that currently votes for traditional right-wing parties and the working class who vote for Le Pen. (Many people are surprised that his economic platform is not more "populist" and they think it's because he lacks imagination, but they just don't understand that he is doing that on purpose, because he doesn't want to scare the bourgeoisie.) At least, he is hoping that he can take enough voters on both sides to reach the second round of the presidential election, which unlike Le Pen he would have a chance of winning because — at least that's what he thinks — he is not as toxic as her.

Is he right? That's the million-dollar question. So far, he is doing worse in the polls than Le Pen when they test them against Macron in the second round, but I have a hard time believing that Zemmour could be as toxic as Le Pen after decades of nonstop demonizing of her family and I suspect that it will change as the campaign starts in earnest next year and people who don't follow politics closely get exposed to him. However, this won't matter if he doesn't make it to the second round, and while it's still unclear whether he will at this point he has been doing spectacularly well so far:

I can assure you that, if you had told anyone 6 months ago — including people in Zemmour's campaign — that he'd be at 12%-15% in the polls in December, no one would have believed you. Some people think that he is going to crash in the next few weeks, but while it's possible, I doubt it's going to happen because he now seems to have a solid base of people who tell pollsters they are sure to vote for him. (Only Le Pen and Macron do better than him in that respect.) It's true that after rising incredibly fast in the polls, he started going down about a month ago, but it looks as though he managed to stop the fall. The first round of the election will be decided by the people who hesitate between Zemmour, Le Pen and Pécresse, the candidate of the Republicans, the traditional right-wing party, who recently had a jump in the polls after she won the nomination. However, I personally think Pécresse is going to fall in the polls next year because she is basically a female version of Macron and people will prefer the original to the copy, so that it will be between Le Pen and Zemmour.

Whether Zemmour can make it to the second round will depend on a few things. First, as I noted above, Zemmour has a similar problem with women as Trump, but it's actually a bigger problem for him. Indeed, in the case of Trump, it was compensated by the fact that he was running in a two-party system, so with polarization many women who wouldn't have voted for Trump otherwise ended up voting for him anyway because he wasn't a Democrat. In France, right-wing women have other options (Pécresse and Le Pen), so Zemmour will have to improve his image among women if he wants to have a chance. He will also need to do better among non-college educated voters. On this point, the optimistic hypothesis for Zemmour is that, because they don't follow politics closely, those voters have not been exposed much to his message yet, so that for the moment they just say they intend to vote for Le Pen because they are more familiar with her. However, if that's the explanation for why Le Pen is doing so much better than him among non-college educated voters, it's likely that when the campaign starts in earnest next year and even people who don't follow politics very closely get exposed to his message, Zemmour will make gains at Le Pen's expense in that group. Indeed, it's clear that Le Pen and Zemmour are to a large extent competing for the same voters, since people who say they intend to vote for one are much more likely to cite the other as their second choice than any other candidate. However, it's also possible that non-college educated voters just dislike Zemmour's more intellectual style, in which case this will not happen and it will be difficult for him to reach the second round. Of course, even if he does, he'd still have to convince enough people that he isn't an extremist and that he is ready to govern to win against Macron. Right now, if I had to bet, I'd say that Zemmour's chances of reaching the second round are about 50% and that conditional on making it to the second round his probability of winning is around 30%. This implies a 15% probability that he will be the next president of France, which is pretty close to what betting markets are saying.

Conclusion

There is still a pretty high probability that Zemmour won't even make it to the second round of the presidential election and, even if he does, Macron remains the overwhelming favorite. However, while it's still unlikely, I think the hypothesis that Zemmour will be the next president of France is higher than most people realize. If what I said above is right, it's about 15%, which is low but not so low that it can be totally ignored. Moreover, even if he won, he would still have to defeat the French "Deep State". This won't be easy, but Zemmour is better equipped than Trump was to do it, because as I noted above he has a much better understanding of the issues and has access to more people who are qualified to fill his administration. If he somehow managed to do all that, however, I think it would change a lot of things, not just in France but in Europe. In particular, the ideological balance of power in the EU would be deeply transformed, because it's one thing if a small country like Hungary is governed by a "populist" government but it's quite another if it's the second-largest country in the Union and the only one with a permanent seat on the UN Security Council.

Anti-immigration sentiment has been rising in Europe for several years and even left-wing governments have had to adopt a more restrictionist stance under pressure from public opinion. Zemmour's platform on immigration would necessarily result in a showdown with the EU. Most people seem to think that he would have to back down, but in my opinion they are completely delusional. Public opinion in Europe is overwhelmingly on Zemmour's side on immigration and France leaving the EU would be the end of the Union, something people in Brussels are well aware of, so I think that, as soon as they realize that he is committed to getting what he wants on that issue, they would bend the knee. Of course, for that to happen, Zemmour would have to win first, but this is why you should follow the presidential race closely next year. The stakes have never been so high and, despite what everyone thought a few months ago, it should be very interesting.

A few months ago, I published a post on Delta's transmissibility advantage, in which I argued that commonly accepted estimates of that advantage were likely overestimated and that in any case we didn't have very good reasons to take them at face value. My argument was based on the distinction between a transmission advantage and a transmissibility advantage. A variant has a transmissibility advantage over another if, other things being equal, a person infected by that variant will on average infect more people. It has a transmission advantage if, in some particular context, people infected by it happen to infect on average more people. A variant can have a transmission advantage over another for a number of reasons. One of them is that it has a transmissibility advantage, but that's not the only one. For instance, if a variant was introduced in a social network where most people don't have immunity, it will spread more easily than variants that are circulating in social networks where most people have already been infected or vaccinated and are therefore less susceptible to infection. Thus, it's dangerous to use a variant's transmission advantage to estimate its transmissibility advantage, because if different variants are circulating in different contexts, and we have good reasons to think that's often the case, one of them might have a transmission advantage over the other even if it has no transmissibility advantage, a transmissibility advantage but not as large as its transmission advantage or even a transmissibility disadvantage. The problem is that, in practice, this is exactly what people do. They compare the growth rate of the new variant with that of previously established strains and use that to estimate its transmission advantage. This transmission advantage usually varies wildly across space and time, so they take the average and assume it corresponds to a transmissibility advantage, even if there is no good reason to think so. I also explained why, if people continue to use that method, they will eventually reach absurd conclusions:

If a variant is rapidly taking over, then even if it has no transmissibility advantage or only a modest one, it must have a large transmission advantage during its initial expansion, since otherwise it wouldn’t be taking over rapidly. Thus, if every time a new variant rapidly takes over in many places epidemiologists use its transmission advantage during its initial expansion to estimate its transmissibility advantage (even if the variant’s transmission advantage later collapses), they will eventually conclude that Omega or whatever has a basic reproduction number of 125, at which point it will perhaps finally dawn on them that such a methodology is not particularly reliable.

As it turned out, we didn't even have to wait for Omega, we've reached that point already with Omicron. For instance, here is what Tom Wenseleers, a Belgian professor of biostatistics, said about the expansion of Omicron in South Africa:

To be fair to him, he makes clear later that he is just talking about the effective reproduction number, not the basic reproduction number. In other words, he admits that the data don't necessarily imply a transmissibility advantage, but merely a transmission advantage.

This is because, if we assumed that it reflected a transmissibility advantage, it would mean that Omicron has a basic reproduction number somewhere between 40 and 50 if you accept the estimates of Delta's transmissibility advantage over the original strain that were derived using the same method. Of course, even epidemiologists don't think it's plausible that Omicron is that infectious, so they acknowledge that one can't infer a transmissibility advantage from this transmission advantage. But as I pointed out several months ago, this was already true with Alpha and Delta, because the same method was used to estimate their transmissibility advantages over previously established strains. If this method produced conclusions that are not believable in the case of Omicron, it should cast doubt on the conclusions that were reached about previous variants using the same method. Therefore, the admission that we can't use that method to infer Omicron's transmissibility advantage over Delta has implications that go beyond the debate about how infectious Omicron is, though epidemiologists won't point that out. However, they at least acknowledge that, in the case of Omicron, the inference from a transmission advantage to a transmissibility advantage is not reliable.

But if Omicron isn't 6 times more transmissible than Delta, then how come it's growing so much faster than Delta in South Africa at the moment? One explanation that epidemiologists often advance is that it's better able to evade prior immunity. Indeed, it has several mutations on the spike that are believed to increase transmissibility and the prevalence of immunity has increased in South Africa since Delta took over, so this could certainly be part of the story. However, since as I noted previously the same variant's transmission advantage often varies wildly across space and time even when it doesn't have any advantage in terms of immune evasion or at best a very modest one, it should be obvious that it could be due to number of other factors we don't understand beside the ability to escape prior immunity. In the case of Omicron, since it started to expand at a time when there were only a few hundred cases per day in South Africa and only a fraction of them are sequenced, measurement error could also be a big factor. Daily growth rates are measured by comparing the number of cases from one day to the next, so when you're dealing with very small numbers, even a relatively small increase in absolute terms can result in a very large growth rate. But again there could be a number of factors. To be clear, as I already noted, there are good reasons to think that Omicron is highly infectious because it has several mutations that are associated with more transmissible strains, but there is no way to quantify how transmissible it is by analyzing the mutations it carries.

In any case, it doesn't really matter. If this variant is really significantly more transmissible or better at evading prior immunity than Delta, then it will soon be everywhere and there is nothing we can do about it. Indeed, it has already been detected in several countries outside of Africa, so this wouldn't be surprising. On the other hand, if it's not more transmissible or better at evading prior immunity, there is no point in freaking out and closing borders or implementing other restrictions to prevent it from spreading. As many people have noted, closing borders to people coming from South Africa actually disincentivizes the kind of careful genomic surveillance that allow

ed South African scientists to detect Omicron early and warn the rest of the world about it. But perhaps it would be for the best, since as Richard Hanania noted, if we can't detect new variants until they're already everywhere, it will at least prevent governments in the developed world from taking stupid measures because they panic. Some people suggested that closing borders was a way to "buy time", but it's not clear what for exactly. As I argued a few months ago, SARS-CoV-2 is not going anywhere, it will continue to mutate because evolution doesn't go on vacation and new variants will keep emerging, but immunity – whether induced by infection or vaccination – should still protect us against severe disease, so it makes no sense to freak out every time a new variant that might be more transmissible is detected. This is the world we live in now, so we have to accept it and move on. Buying time doesn't actually buy you anything when there is no finish line.

Summary

• Standard epidemiological models predict that, in the absence of behavioral changes, an epidemic should continue to grow until herd immunity has been reached and the dynamic of the epidemic is determined by people's behavior.

• However, during the COVID-19 pandemic, there have been plenty of cases where the effective reproduction number of the pandemic underwent large fluctuations that, as far as we can tell, can't be explained by behavioral changes.

• While everybody admits that other factors, such as meteorological variables, can also affect transmission, it doesn't look as though they can explain the large fluctuations of the effective reproduction number that often took place in the absence of any behavioral changes.

• I argue that, while standard epidemiological models, which assume a homogeneous or quasi-homogeneous mixing population, can't make sense of those fluctuations, they can be explained by population structure.

• I show with simulations that, if the population can be divided into networks of quasi-homogeneous mixing populations that are internally well-connected but only loosely connected to each other, the effective reproduction number can undergo large fluctuations even in the absence of behavioral changes.

• I argue that, while there is no evidence that can bear directly on this hypothesis, it could explain several phenomena beyond the cyclical nature of the pandemic and the disconnect between transmission and behavior – why the transmission advantage of variants is so variable, why waves are correlated across regions, why even places with a high prevalence of immunity can experience large waves – that are difficult to explain within the traditional modeling framework.

• If the population has that kind of structure, then some of the quantities we have been obsessing over during the pandemic, such as the effective reproduction number and the herd immunity threshold, are essentially meaningless at the aggregate level.

• Moreover, in the presence of complex population structure, the methods that have been used to estimate the impact of non-pharmaceutical interventions are totally unreliable. Thus, even if this hypothesis turned out to be false, we should regard many widespread claims about the pandemic with the utmost suspicion since we have good reasons to think it might be true.

• I conclude that we should try to find data about the characteristics of the networks on which the virus is spreading and make sure that we have such data when the next pandemic hits so that modeling can properly take population structure into account.

The COVID-19 pandemic has been ongoing for more than one year and a half now, but we still don’t understand its dynamic well. What is perhaps more surprising, however, is that the fact that we don’t understand it well is not more widely acknowledged. For the most part, governments continue to rely on projections based on models that have systematically proved to be massively unreliable, while this fact receives almost no attention in the public debate. Occasionally, one can hear people briefly acknowledge that we don’t really understand why waves of infections come and go (typically after the epidemic took a turn that wasn’t predicted by the models used to make projections), but they almost never follow up with a real effort to try and figure out why the pandemic exhibits this cyclical pattern. People often claim that it’s because respiratory infections are “seasonal”, but meteorological variables are not associated with transmission strongly enough to explain this pattern, so in practice this boils down to the claim that infections rates fluctuate over time, which is not a genuine explanation but just a restatement of what is to be explained. In theory, transmission should ultimately be determined by people’s behavior, but the effective reproduction number often fluctuates wildly even when, as far as we can tell with the data we have, there were no behavioral changes.

In this post, I propose that such fluctuations could be the result of population structure, which is mostly ignored in the models used in applied work on the pandemic. Indeed, while standard epidemiological models assume that the virus spreads in a homogeneous or quasi-homogeneous population (i. e. that infectious people have the same probability of infecting anyone else in the population or at least in their age group), this is a very crude idealization. In reality, the virus spreads on a complex network, which depends on people’s patterns of interactions. I show with simulations that, if real populations depart sufficiently from the homogeneous mixing assumption, the effective reproduction number can undergo large fluctuations even in the absence of behavioral changes. I argue that, although we don’t have evidence bearing directly on this hypothesis, in addition to the disconnect between transmission and behavior that has often been observed, it could explain several other puzzling phenomena. Finally, I show that if real populations really have the kind of structure posited by my theory, then the methods used in the literature to estimate the effects of non-pharmaceutical interventions are totally unreliable. Thus, even if that hypothesis turned out to be false, as long as we have good reasons to believe it might be true, we should take the conclusions of studies on the impact of non-pharmaceutical interventions, many of which are of dubious quality even if we ignore the issue of population structure, with a large grain of salt.

What epidemics are supposed to be like according to standard epidemiological models

There are many different approaches to model the spread of infectious diseases, but the most commonly used models are compartment models, which are called that because they divide the population into several compartments and model the way in which individuals move from one compartment into another in the course of the epidemic. For instance, the Susceptible-Infectious-Recovered (SIR) model, which is arguably the most famous epidemiological model, divides the population into 3 compartments. At the beginning of the epidemic, everyone is susceptible, but after the virus is introduced in the population people start infecting each other and move into the infectious compartment, then finally into the recovered compartment when they are no longer infectious and can no longer be infected because they have become immune. Variants of this model can be obtained by adding or removing compartments and transitions between them, which makes this approach very flexible. For instance, the Susceptible-Exposed-Infectious-Recovered (SEIR) model adds a compartment for people who have been exposed but are not yet infectious because they are still in the incubation period, as well as a transition between the exposed and infectious compartments. Of course, the SIR model can also be adapted to take vaccination into account, which reduces the share of the population susceptible to infection.

In this post, I will use a closely related model, which is essentially a stochastic, discrete-time version of the SIR model with overdispersion. Don’t worry if this sounds like gibberish to you, the model is actually very simple and the way in which it works can be explained without complicated jargon. The key quantity governing the dynamic of the epidemic in the model is the basic reproduction number. It’s the average number of people that someone who is infected would infect during their infectious period if everyone in the population were susceptible. It must be distinguished from the effective reproduction number, which is the actual number of people that people who are infected will infect on average. The effective reproduction number is always lower than the basic reproduction number, because not everyone is susceptible in the population, so some people that would have been infected after interacting with someone infectious will not actually be infected because they are no longer susceptible. The model assumes that everyone has immunity after they have been infected and that everyone in the population interacts with everyone else randomly. Thus, if the basic reproduction number is 3 and at one point during the simulation 50% of the population has already been infected, the effective reproduction number at that point is only 1.5, because on average 50% of the people that infectious people interact with can no longer be infected. At the beginning of the simulation, the population is seeded with a few infected people to get the epidemic started. On each day, the model randomly draws the number of people that each person infected on that day will eventually infect from a negative binomial distribution with a mean equal to the effective reproduction number on that day and a dispersion parameter of 0.1, so as to model superspreading.1 Then, for each secondary infection caused by a person infected on that day, it randomly draws how much time later this secondary infection takes place from a gamma distribution with a mean of 4.8 days and a standard deviation of 1.7 days.2 This process is repeated until the end of the simulation.

This graph shows how a typical epidemic unfolds in that model with a basic reproduction number of 3 in a population of 10 million:

As we shall see, a crucial assumption of this kind of model, which is called the homogeneous mixing assumption, is that people interact and infect each other randomly. However, as long as that assumption holds and even when it’s somewhat relaxed, a compartment model will always generate a qualitatively similar epidemic if the basic reproduction number remains constant and the immunity acquired by people who have recovered doesn’t wane. In other words, while the height of the curve at the peak and the area under it may vary depending on what assumptions were made, it will always have this kind of shape as long as the basic reproduction number remains constant, immunity doesn’t wane and the homogeneous mixing assumption or something close enough to it holds.

As we have seen, the basic reproduction number is the number of people that each infected individual will infect on average when everyone in the population is susceptible. It depends on how many contacts infectious people have and how often those contacts result in transmission of the virus. Thus, in a framework where immunity is assumed to be permanent and the homogeneous mixing assumption is made, the basic reproduction number only depends on people’s behavior. It goes up when people have more contacts with each other or have contacts that are more likely to result in transmission of the virus and goes down if they have fewer contacts or have contacts that are less likely to result in the transmission of the virus. This is a key assumption of the standard modeling framework, so it’s important to understand this point, because as we shall see shortly there are good reasons to doubt that it’s true. As I already noted, in the simulation that was used to generate the epidemic depicted on the graph shown above, the basic reproduction number was assumed to be equal to 3. A population of 10 million was seeded randomly with a few infections during the first 30 days of the simulation and some of them started chains of infections that eventually resulted in the large epidemic shown in the graph. The basic reproduction number was assumed to remain constant over time, which is equivalent to assuming that people didn’t change their behavior during the course of the epidemic or at least not in a way that affected the basic reproduction number.

As you can see on the graph, during the initial phase of the epidemic, the daily number of infections — which is called “incidence” — is growing exponentially. This makes sense because, while everyone or almost everyone is still susceptible, each person infects 3 people on average after being infected, each of whom then go on to infect 3 people on average, etc. However, as the epidemic grows, the average number of people infected by infectious individuals, which as we have seen is called the effective reproduction number (as opposed to the basic reproduction number that would obtain if everyone were susceptible), goes down since more and more of the people they interact with and would have infected when everyone was susceptible have immunity because they have already been infected previously. Eventually, the epidemic reaches a point where each person only infects 1 other person after they have been infected, which is called the herd immunity threshold. If the basic reproduction number is 3 as I have assumed in the simulation, the herd immunity threshold is reached when 2/3 of the population has already been infected and is no longer susceptible, because at this point 2 out of 3 people that would have been infected by each infectious person have immunity and can’t be infected anymore. Once the herd immunity threshold has been crossed, incidence starts to go down, until eventually it reaches zero and the epidemic is extinguished.

This is what happens when the basic reproduction number stays constant, but things are different if people voluntarily change their behavior or are forced to do so by the government.3 For instance, suppose that initially the basic reproduction number is 3, but that on the 50th day of the simulation the government declares a lockdown for 60 days, which temporarily brings down the basic reproduction number to 0.75 before it goes back to 3 after the lockdown is lifted.4 This graph shows the result of a simulation under this scenario with the same model as before:

As you can see, after the lockdown comes into effect, incidence starts to go down.5 However, exponential growth resumes as soon as the lockdown is lifted, which results in a very large second wave. This wave only starts receding when the herd immunity is reached, which as before happens when 2/3 of the population has been infected, since after the lockdown is lifted the basic reproduction number goes back to 3 because we’re assuming that people only changed their behavior in response to restrictions.

As I already noted, there are many variants of the SIR model, but they exhibit the same qualitative behavior in almost every case. This is true even when the homogeneous mixing assumption is somewhat relaxed. For instance, the herd immunity threshold in the SIR model is (where is the basic reproduction number), but it’s lower in a model that divides the population into groups of people who differ in how much social activity they have. However, even in such a model, incidence keeps growing until the herd immunity threshold is reached and can no longer grow after that threshold has been reached. Thus, while the height of the epidemic curve and the area under it may be different in different models, as long as they assume that immunity doesn’t wane and do not depart too much from the homogeneous mixing assumption, the epidemic curve always has the same basic shape, with a phase of exponential growth that gradually slows until the peak corresponding to the herd immunity threshold is reached, after which incidence starts decreasing until it reaches zero and the epidemic is extinguished. Moreover, even if the basic reproduction number is temporarily reduced by non-pharmaceutical interventions or voluntary behavior change and the effective reproduction number drops below 1 in such a model, incidence starts growing again as soon as the basic reproduction number goes back to its previous level unless the herd immunity threshold has been reached or the number of infected people has dropped to zero before that.6

Standard epidemiological models fail to explain the dynamic of the COVID-19 pandemic

As we have just seen, based on the SIR model and most of its variants, we would expect the COVID-19 pandemic to exhibit a specific type of dynamic. In particular, as long as the population is still far from the herd immunity threshold, the epidemic should grow quasi-exponentially unless people change their behavior in a way that affects the basic reproduction number. However, if we look at real data during the COVID-19 pandemic, we see that actual epidemic behavior radically departs from this prediction. First, as I noted previously, there are many cases in which incidence started to fall long before the herd immunity threshold could plausibly be assumed to have been reached and despite the absence of a lockdown or other stringent legal restrictions. The most famous example is what happened in Sweden during the first wave, but it’s not a very good example if we’re trying to show that standard epidemiological models can’t explain the data because there is very good evidence that people in Sweden engaged in massive voluntary behavioral changes despite the absence of stringent restrictions:

As you can see, the daily number of ICU admissions for COVID-19 started to fall in early April, which suggests that incidence started to fall about 2 weeks before that.7 But as I noted above, this graph also shows a large reduction of mobility around the same time. Thus, if this reduction of mobility was associated with behavioral changes that resulted in a reduction of the reproduction number (which is likely because it’s hard to imagine that such a large reduction in mobility was not accompanied by a reduction in the number of contacts people had with each other), it’s not surprising that incidence fell despite the lack of stringent restrictions, since that’s exactly what standard epidemiological models in which the basic reproduction number is allowed to vary predict.8

However, there are many examples where the same thing happened, but without any evidence that voluntary behavioral changes could explain why incidence started to fall even though herd immunity was still a long way. For instance, it happened in Florida during the summer of 2020, where there was a large wave of infections that peaked in the middle of July:

A variety of restrictions were in place during this period in Florida, which varied on a county-by-county basis, but in most places they were implemented in June or at the beginning of July and remained in place until after the wave had peaked, so non-pharmaceutical interventions can’t explain why incidence started falling in mid-July.9 Moreover, as you can see on the chart, while mobility was significantly reduced compared to the pre-pandemic period, there was virtually no change in mobility except for a temporary drop around the Fourth of July. I could make the same point about the wave of infections that Florida experienced last winter, which receded in January before vaccination could possibly have made any difference, while there were virtually no restrictions and despite the fact that mobility didn’t change during that period except for Christmas and New Year’s Day.

Another example is what happened in Spain last winter when the country experienced a very large wave, yet the government refused to order another lockdown, as it had during the first wave. Local governments did put in place a variety of restrictions, but the national government prevented them from ordering a regional lockdown and, in some regions, restrictions remained minimal during most of the period. In particular, this was the case in Madrid, but it didn’t prevent incidence from peaking around the same time as in the rest of Spain:

The only significant change in the legal restrictions that applied in Madrid during this period was a set of new rules, including a curfew between 11 pm and 6 am, that came into effect on January 18, but taking into account the incubation period the peak of infections almost certainly happened before that. Moreover, as you can see in the upper panel of the chart, this didn’t have any detectable effect on mobility. The fact that incidence started to fall around the same time in Spain, despite the wide variety of restrictions that local governments imposed in different regions, also suggests that government intervention wasn’t a key factor. If we look at mobility, which captures behavioral changes regardless of whether they were voluntary or induced by restrictions, there was a drop associated with Christmas, New Year’s Day and the Epiphany, as well as a significant fall that lasted for about a week after the Epiphany and was presumably caused by the snowstorm that paralyzed Madrid for several days at the time. In theory, this could have temporarily reduced transmission, but since mobility started to reverse to previous levels as soon as the snow was cleared from the streets this reduction should have been temporary and standard epidemiological models predict that epidemic growth should have quickly resumed. However, that is not what happened, since incidence continued to fall after that and didn’t rise again until the end of March. Vaccination also couldn’t possibly explain why the epidemic receded since it was still progressing at a very slow pace in Spain at the time and, even by the end of January, only 0.8% of the population was fully vaccinated.

Thus, incidence often starts falling long before it should according to standard epidemiological models, but it also starts to rise when, according to the same models, it should not. The debate has focused on what makes waves of infections recede, but if we’re trying to understand the dynamic of the epidemic, the question of why incidence rises when it does is just as important. Sometimes, it seems that incidence starts blowing up for no particular reason, since none of the factors that are assumed to govern the dynamic of the epidemic by standard epidemiological models have changed. For instance, France experienced a large wave of infections last fall, yet neither changes in restrictions nor changes in mobility can explain why the epidemic growth exploded when it did:

As you can see, incidence plateaued in September before suddenly exploding in October, but there were no non-pharmaceutical interventions until mid-October and mobility doesn’t seem to have changed before that.

In this case, I think it’s illuminating to also compare mobility to the effective reproduction number and not just the daily number of cases, because it illustrates the fact that restrictions and voluntary behavior changes can’t explain the way in which transmission changes over time:

As you can see, the effective reproduction number fell sharply in September before increasing rapidly at the beginning of October (which led to a large wave of infections and ultimately the second lockdown), but again there were virtually no restrictions until mid-October in France and it doesn’t seem that changes in mobility can explain those fluctuations either.10

I could literally go on for hours about other similar examples, which are difficult to reconcile with the way epidemics are supposed to behave according to standard epidemiological models, but you get the idea. In general, when looking at data on the COVID-19 pandemic, it’s striking how volatile the effective reproduction number is and how little of those fluctuations make sense within a framework that assumes that, as long as the population isn’t close to herd immunity, the dynamic of the epidemic is driven by changes in behavior, whether voluntary or induced by non-pharmaceutical interventions. This conclusion is not the result of cherry-picking, since it’s also clear when you perform more systematic analyses. Indeed, while many studies reported a strong correlation between mobility and epidemic growth early in the pandemic, this association became very weak almost everywhere after the first wave.11 There seem to be other factors besides changes in behavior that have a large effect on the dynamic of the epidemic. However, the overwhelming majority of epidemiological models used to study the pandemic don’t take into account any other factors, so it’s unsurprising that they have performed so abysmally. It’s well-known that, when incidence is low, stochastic factors can play a large role, but this can’t be the explanation for the large fluctuations of the reproduction number we observe in the data that are not accounted for by changes in behavior since, as we have just seen, such fluctuations were often observed during periods when incidence was high.

Among the factors that have been put forward to explain the fluctuations of the effective reproduction number, this only leaves meteorological variables. However, while I do not doubt that meteorological variables affect transmission, I don’t think they can explain the large fluctuations that the effective reproduction number often undergoes even in the absence of behavioral changes. First, while several studies have found a relationship between meteorological variables and the effective reproduction number, the association seems relatively weak.12 Indeed, places with very similar climates have experienced waves of infections at very different times of the year, while places with completely different climates have experienced waves at the same time, which should already make clear that meteorological variables only have a limited impact even without looking at the data in a more systematic way. Moreover, to the extent that meteorological variables affect transmission, we expect their effect to be at least partly mediated by people’s behavior. Indeed, meteorological variables can in theory have both a direct and indirect effect, but only the former is independent from behavior. The direct effect is the effect that meteorological variables have on the mechanism of transmission at the biochemical level, while the indirect effect is the effect they induce by causing behavioral changes. Indeed, as we have seen above in the case of the snowstorm that paralyzed Madrid for several days last January, weather affects people’s behavior, which in turn can affect transmission. Since part of the effect of meteorological variables on transmission is mediated by people’s behavior, it’s even more unlikely that meteorological variables could explain why the effective reproduction number often undergoes large fluctuations even in the absence of meaningful behavioral changes. This suggests that standard epidemiological models can’t be fixed by taking into account more variables, but that a more fundamental change of framework is called for.

Of course, if you are really committed to standard epidemiological models, you can always come up with a story to reconcile the data with those models. For instance, in my discussion so far, I have used mobility as a proxy for the behavioral variables that affect transmission, but one could object that data on mobility don’t reflect the relevant behavioral changes and that it’s therefore wrong to infer from the weak association between mobility and epidemic growth that behavior can’t explain the dynamic of the epidemic. It could be that, with better data on people’s behavior, we’d find a stronger association between behavioral changes and the effective reproduction number. A recent study based on GPS tracking data from over 1 million cellphones in Germany suggests that, with more fine-grained data, we may indeed be able to do that. The authors used the data to determine when people were physically close to each other, considered it a contact when they remained close for long enough and used that to construct a graph of people’s contacts. Based on that graph, they were able to compute not only the average number of contacts over time, but also what they call a “contact index” that takes into account both the average number of contacts and its variance. They also computed this index because theoretical results suggest that heterogeneity of contacts and not just the mean number of contacts people have affect the epidemic’s reproduction number. They show that, while the average number of contacts is poorly correlated to the effective reproduction number after the first wave, the contact index remained predictive of the effective reproduction number after that.13 Of course, this study has many limitations (starting with the fact that it’s limited to data about Germany), but I think it’s nevertheless a very important paper that has unfairly been ignored and hopefully this post can help rectify that.

This study provides some evidence for the claim that, while aggregate mobility data is not very predictive of the effective reproduction number, we’d be able to find a stronger association between transmission and behavior if we had more fine-grained data on the latter. However, while I have no doubt that mobility data are a very imperfect proxy for the relevant behavioral changes and that we’d find a stronger association between the effective reproduction number and behavior with better data, the disconnect between mobility and epidemic growth is so extreme in so many cases that I find this response totally unconvincing if it’s meant to imply that, except for a small part of the variability that can be explained by factors such as meteorological variables, behavioral changes are sufficient to explain the fluctuations of the effective reproduction number. In general, it’s always possible to protect any theory against falsification if you’re willing to add enough epicycles to it, but it doesn’t mean that it’s reasonable to do so. If there were just a few anomalies in the data, it would make sense to explain them away by assuming that a few unknown factors that generally play a small role sometimes conspire to falsify standard epidemiological models that don’t take them into account, but anomalies are ubiquitous so I think it’s clear that something else is going on here.14 Everywhere waves come and go in a way that is impossible to reconcile with the predictions of standard epidemiological models without tying yourself into knots and the effective reproduction number frequently undergoes large fluctuations that can’t be explained by changes in behavior. While epidemiologists have mostly ignored this fact and continue to use models that have systematically and massively failed, I think it’s time to accept it and try to understand what, in the absence of meaningful behavioral changes, could explain the large fluctuations of the effective reproduction number that we have observed.15

Population structure as the missing piece of the puzzle

At this stage, we seem to be faced with a dilemma. On the one hand, as we have seen, the effective reproduction number of the epidemic frequently undergoes large fluctuations even in the absence of behavioral changes. On the other hand, we have strong theoretical reasons to expect that ultimately transmission depends on people’s behavior, since we know that SARS-CoV-2 transmits by contact. Thus, it seems that any theory that can explain why the effective reproduction number can undergo large fluctuations even in the absence of meaningful behavioral change must deny this basic fact about the mechanism of transmission, making it a non-starter. In this section, I will try to square this circle by presenting a theory that, while consistent with the fact that SARS-CoV-2 is transmitted by contact and therefore that ultimately transmission depends on people’s behavior, explains why large fluctuations of the effective reproduction number can nevertheless occur even in the absence of meaningful behavioral changes. The first thing to consider is that, from the fact that SARS-CoV-2 is transmitted by contact, it doesn’t follow that large fluctuations of the effective reproduction number can only result from large behavioral change. In fact, I have already implicitly acknowledged that fact above when I said that meteorological variables probably affect transmission, even if their effect doesn’t seem large enough to explain the large fluctuations of the effective reproduction number that we frequently observe even in the absence of behavioral changes.16 Another example of a factor that could affect transmission even if people don’t change their behavior is the emergence of more transmissible variants. As I argued previously, I think that Alpha’s and Delta’s transmissibility advantages over the previously established strains have been vastly overestimated, but you don’t have to agree with me on that to agree that it can’t be the whole story behind the disconnect between transmission and behavior. Indeed, as the examples I used above show, the effective reproduction number has often undergone large fluctuations in the absence of meaningful behavioral changes even when the distribution of variants remained stable. So there must be another factor that explains this phenomenon and, in this section, I will propose that it’s population structure.

As we have seen, in order to study the spread of infectious diseases, epidemiologists use models that make various simplifying assumptions. In particular, they typically assume a homogeneous mixing population, which means that contacts between people are totally random, so everyone is equally likely to infect everyone else if they are infected.17 However, this assumption is totally unrealistic, because in the real world transmission occurs in a highly structured population and contacts are not random. If you are infected, the probability that you are going to infect most people in the population is effectively zero, because you’ll never have any contact with them. Of course, there are many people you will never have any contact with, but whom you could nevertheless indirectly infect by starting a chain of infections that goes through them, but for most people the probability that this will happen is infinitesimal, whereas it’s much higher for people you interact with often because they are your colleagues, friends, members of your family, etc. and people who frequently interact with them. In reality, the virus doesn’t spread in a homogeneous mixing population, but in a highly structured one where each individual has different patterns of interactions with different people. How the virus spreads depends on who interacts with whom, how often they interact and what type of interaction they have, since those facts determine what chains of infections can exist and how likely each of them is depending on where the virus starts from in the population.

Thus, while standard epidemiological models represent the population as a collection of particles that interact randomly with each other, it’s better seen as a complex network where nodes are individuals and edges represent potential interactions between them that could result in transmission. Each edge in the network has a weight that indicates how easily transmission can occur along that edge if one of the individuals it connects happens to be infectious, which is determined by the frequency and nature of the contacts between them. Epidemiologists of infectious diseases have produced a voluminous literature on models that assume a virus spreads on these kinds of networks, so it’s not as if they didn’t know that real epidemics don’t spread in a homogeneous mixing population and hadn’t studied how population structure can affect transmission, but this literature had essentially no effect on applied work during the pandemic, perhaps because the kind of data that would be necessary to model real epidemics in that way is almost never available.18 Yet I think that population structure could hold the key to the mystery I have identified above, namely that the effective reproduction number often undergoes large fluctuations that, as far as we can tell, can’t be explained by changes in people’s behavior. Indeed, what I’m proposing is that we can solve this mystery by postulating that the network on which the epidemic spreads has what in network science is called “community structure”, which means that it can be divided into subnetworks whose nodes are internally densely connected while the subnetworks are only loosely connected to each other.

To illustrate this concept, here is a graph I found in this paper that shows the friendship network of a few thousand people on Facebook, where community structure is clearly visible:

Of course, the networks on which the COVID-19 epidemic spreads are far more complicated, since they can involve millions of people. Moreover, the edges between nodes don’t have the same meaning, since you can be friends with someone on Facebook but never have any interaction with them that could result in transmission of the virus and you can have that kind of interaction with someone you aren’t friends on Facebook with. But fundamentally what I’m proposing is that, when the epidemic spreads in a country, it does so in a network that has this kind of structure.

But how would that explain why the effective reproduction number of the epidemic can undergo large fluctuations even when people’s behavior doesn’t change? Well, if the virus is introduced in a network of this type, it will spread easily within the subnetwork where it has been introduced, but it will have a harder time leaving that subnetwork to spread into others, because subnetworks are loosely connected to each other. As it spreads through a subnetwork, the prevalence of immunity will increase in that subnetwork and, unless it manages to reach another subnetwork from there, the effective reproduction number of the epidemic will go down. When the virus is introduced in another subnetwork where the prevalence of immunity is low, either because that subnetwork has been seeded from the outside or because the virus managed to reach it from another subnetwork through one of the edges connecting them, the effective reproduction number will go up again and so will incidence, until that subnetwork is also saturated. Thus, if the population has that kind of structure, waves of infections will tend to be restricted to one or a few subnetworks, which in turn would explain why they come and go even when people don’t change their behavior. On this hypothesis, the virus is still transmitted by contact and therefore transmission still depends on people’s behavior, so it’s consistent with what we know about the basic mechanics of transmission, but how behavior at the individual level translates into the effective reproduction number at the aggregate level depends on population structure. This theory can therefore solve the dilemma I identified at the beginning of this section of the apparent impossibility of reconciling our knowledge of the mechanics of transmission at the individual level with the data at the aggregate level. In short, according to it, population structure was the missing piece of the puzzle.

Simulating the effect of population structure on transmission

The claims I just made about how population structure affects transmission seem intuitively plausible, but intuition can be misleading, so in this section I’m going to present the result of simulations that confirm that, when the network that encodes the information about people’s interactions can be divided into subnetworks that are internally densely connected but only loosely connected to each other, the effective reproduction number of the epidemic can undergo large fluctuations even if we assume that people’s behavior doesn’t change.19 Instead of simulating the spread of the virus on a network of individuals, which is very computationally intensive if the network is large, I assumed that parts of that network could be considered homogeneous mixing populations and modeled the spread on a network of subpopulations. I construct the network in such a way that it can be divided into subnetworks containing subpopulations that are well-connected to each other, but only loosely connected to subpopulations in other subnetworks. Since I assume that each subpopulation in the network is approximately homogeneous mixing, the spread of the virus within each subpopulation is modeled with the stochastic, discrete-time SIR-type model I described in the first section. However, people who have been infected in one subpopulation can spend their infectious period in another, as long as the subpopulation to which they belong is connected to it. I came up with this approach on my own when I started thinking about this, but it turns out that it’s similar to what epidemiologists call metapopulation modeling, which is not surprising since it’s a very natural way of modeling population structure. However, in the literature on that kind of models, subpopulations are often interpreted as spatially separated from each other, whereas for reasons I will explain later I make no such assumption.

I assume the population is divided into 100 subnetworks and randomly draw the number of subpopulations each of them contains from a Poisson distribution with a mean of 100. This resulted in a network of 10,105 subpopulations distributed across 100 subnetworks. The size of each subpopulation is randomly drawn from a discrete power law with a minimum size of 250 and a scaling parameter of 2.9. The result is that subpopulations have a size of about 520 on average, for a total population of approximately 5.2 million, but the vast majority of subpopulations are smaller than that while a few are much larger because power laws are fat-tailed. Each subnetwork is generated randomly using a method called the configuration model.20 Roughly, the number of edges connected to each node — which is called the degree of that node — is randomly drawn from a Poisson distribution with a mean of 5, then nodes are connected to each other randomly so as to respect this pre-defined degree distribution.21 Once the subnetworks have been generated, it remains to connect them to each other. In order to do so, for each subnetwork, I first randomly draw the number of edges connecting a node in that subnetwork to a node in another subnetwork, which can be seen as the analogue of the degree of a node for subnetworks, from a Poisson distribution with a mean of 5. Then, I randomly pick a node in one subnetwork and connect it to a randomly chosen node in another subnetwork, so as to respect this pre-defined degree distribution.22 The result is a network that can be divided into subnetworks that are internally densely connected, but only loosely connected to each other.23

Here is a visualization of the network that was generated by this procedure and used for the simulation whose results I’m going to present shortly:

In order to make the community structure easier to visualize, I assigned a different color to each subnetwork and used a graph drawing algorithm to cluster the nodes by subnetwork.24

Connectivity in the relevant sense doesn’t only depend on the number of edges connecting different subpopulations, but also on the probability that someone who belongs to one subpopulation will travel along one of those edges to another subpopulation and spend their infectious period over there.25 Thus, in order to model that, each edge is assigned a weight that corresponds to the probability that someone who has been infected in one subpopulation will travel along that edge and spend their infectious period in another subpopulation. I used a weight of 0.05 for within-subnetwork edges and a weight of 0.0001 for between-subnetwork edges. In other words, infectious people in one subpopulation have a 5% chance of spending their infectious period in each of the subpopulations in the same subnetwork to which it’s connected, while they have a probability of 1 in 10,000 of spending their infectious period in each of the subpopulations in a different subnetwork to which it’s connected. Thus, the virus can travel much more easily within subnetworks than between them, since nodes within the same subnetworks are both more densely connected and the edges connecting them have a greater weight than nodes belonging to different subnetworks. Nevertheless, by the time a subnetwork has been completely saturated by the virus, the probability that it has traveled to another subnetwork from there — where it may or may not start a large outbreak — is about 25%, so it’s hardly impossible and will often happen.26

I seed the population randomly at a constant rate for the whole duration of the simulation and, on each day, infected people from the outside are randomly distributed across subpopulations.27 You can think of the population I’m modeling as a country that is being continuously and randomly seeded from abroad at a constant rate. This isn’t very realistic, because in reality the rate at which a country is seeded depends on the state of the epidemic in other countries to which it’s connected and which subpopulation is seeded is not random but depends on what connections they have to foreign countries, but it’s good enough for my purposes in this post.28 The basic reproduction number in each subpopulation was randomly drawn from a normal distribution with a mean of 2.5 and a standard deviation of 0.1 and was assumed to stay constant for the duration of the simulation. Here is a graph that shows the results of the simulation at the level of the population as a whole:

As you can see, at the aggregate level, the effective reproduction number undergoes large fluctuations and several waves of infections come and go, yet behavior didn’t change since we assumed a constant basic reproduction number in each subpopulation and the fluctuations of the effective reproduction number at the aggregate level are purely the result of population structure.

In order to help you get a more intuitive grasp of what is happening, I made this animation that shows how the virus spreads across subpopulations, which are represented by rectangles whose area is proportional to their size inside larger rectangles that represent the subnetworks to which they belong:

As you can see in this animation, once a subpopulation is invaded, the virus quickly spreads to the other subpopulations in the subnetwork to which it belongs. Different subnetworks are invaded at different times, either because the virus managed to spread to them from another subnetwork or because they were seeded from abroad, so what we are seeing at the level of the population as a whole is really the result of aggregating several distinct though linked epidemics. By the end of the simulation, only 27.6% of the population has been infected. Yet, as you can see in that animation, many subnetworks are still untouched by the time it’s over. Thus, if any of them were seeded with the virus, it would likely result in another wave.

Within each subpopulation, the epidemic is progressing as standard epidemiological models predict and if we plotted the epidemic curve it would look like the curve I showed in the first section, but once aggregated they produce something completely different. When the virus is spreading in subpopulations where most people are susceptible, the effective reproduction number for the population as a whole goes up, but it goes down if most of the infections are taking place in subpopulations where a lot of immunity has accumulated. Of course, the accumulation of immunity in some subpopulations can also be more or less balanced out by the fact that the virus started to spread in subpopulations where almost everyone is susceptible because they had so far been spared, in which case the effective reproduction number for the population as a whole remains pretty stable. Depending on the topology of the network and stochastic factors, the model can produce all sorts of epidemic curves at the aggregate level, not just waves that come and go in relatively quick succession but also long periods during which incidence remains high, as we have also seen in some countries. But this variety of epidemic behavior at the aggregate level has nothing to do with behavioral changes, since at the level of subpopulations behavior and therefore the basic reproduction number is assumed to be constant. Thus, simulations confirm that, if the population is divided into networks of subpopulations that are internally densely connected but only loosely connected with each other, the effective reproduction number can undergo large fluctuations even if people’s behavior doesn’t change, as seems to happen in the real world.

Unsurprisingly, if we increase the connectivity between subnetworks enough, the model behaves more like a model with homogeneous mixing. For instance, if I use the same method to generate a network but multiply the average number of edges between subnetworks by 10 and the weight of those edges by 100, I obtain this epidemic:

However, unless we increase connectivity between subnetworks a lot, the model’s behavior remains very different from that of a model with homogeneous population mixing and, as we shall see, this has radical implications.

The relationship between the model and the real world

Of course, the fact that simulations based on this model generate epidemics that are similar to real data doesn’t mean that the model accurately describes reality and, to be clear, I have no doubt that it leaves out a lot of factors that matter. First, even if I’m right that populations have the sort of structure posited by the model, it’s certainly not the case that, as the model assumes, people’s behavior doesn’t change in a way that affects transmission. Indeed, as I already noted, the fact that the effective reproduction number sometimes undergoes large fluctuations even in the absence of behavioral changes doesn’t mean that behavioral changes doesn’t affect transmission. Not only can it do so by changing the basic reproduction number at the level of subpopulations, but it can also do so by modifying the network. Indeed, while I have assumed for the simulation that the network was constant, a more realistic model would use a time-varying network where, as people change their behavior, some edges can appear or disappear and the weight associated to them can change. I have only assumed that the basic reproduction number at the level of subpopulations was constant and that the network didn’t change over time because I wanted to show that, even in the absence of behavioral changes, population structure alone could result in large fluctuations of the effective reproduction number, but I obviously don’t believe that population is the only factor and that people’s behavior doesn’t matter. In fact, not only is the hypothesis that population structure explains some of the fluctuations of the effective reproduction number not inconsistent with the hypothesis that behavioral changes does, but they are complementary because, as I just noted, taking into account population structure allows one to see that behavior can affect transmission not just by modifying the rate at which transmission occurs along the edges of the network but also by modifying the network itself.

Moreover, the hypothesis that populations are structured in the sort of way assumed by the model is hardly obvious and, until we have evidence bearing directly on that, it will remain a conjecture. Unfortunately, we may never have evidence bearing directly on that, because it’s doubtful that we’ll ever have the kind of data we’d need to construct a graph that summarizes the pattern of interactions between individuals that can result in transmission.29 One reason to be skeptical of this hypothesis is that, in most countries, waves of infections have been synchronized to a significant extent across regions. For instance, here is a figure that shows the daily number of infections over time in each French department relative to the maximum incidence reached in that department over the whole period, which starts after the first wave and runs until now:

As you can see, waves of infections tend to be synchronized across departments, but the extent to which this is true varies a lot depending on the wave. Thus, incidence peaked around the same time in almost every department during the second wave (at the beginning of November of last year), but there was less synchronicity during the third wave (which peaked between the end of March and April of this year) and even less during the fourth wave (which peaked in August of this year). The dataset doesn’t cover the first wave, but judging from the data on deaths, the amount of synchronicity it exhibited must have been somewhere between the third and fourth wave. I used French data to illustrate this point, but data from other countries show something very similar.

Now, for the kind of population structure I have suggested to explain this synchronicity, it has to be the case that subpopulations inside each subnetwork are distributed across several regions, because otherwise incidence would peak at very different times in different regions and waves would not be correlated across regions as much as they are. In other words, the population in each region must be distributed into different subnetworks that cut across regional boundaries, which many people will no doubt find implausible. For instance, what this means is that the population is structured in such a way that it’s sometimes easier for the virus to spread from a part of the network consisting of people who live in Paris to another part of the network consisting of people who live in Bordeaux than for it to spread from the former to another part of the network consisting of people who also live in Paris, even though Bordeaux and Paris are several hundreds of kilometers apart. Now, to be clear, I do not deny that intuitively this seems implausible. In fact, when I first considered the possibility that population structure might explain the cyclical dynamic of the epidemic about a year ago, I rejected it precisely for that kind of reasons, but I changed my mind since then for several reasons. First, while this objection has intuitive force, I don’t think we have any reason to trust our intuition on this issue. Indeed, each one of us is only familiar with a minuscule part of the network since we only know what kind of interactions we have with a handful of people and at best what kind of interactions some of them have with even fewer people, but in order to know whether the population has that kind of structure we’d have to be able to know the whole network, so I don’t see why anyone should trust their intuition on this question. In the absence of data bearing directly on that issue, the only thing we can go off is explanatory power, but I don’t know any other theory that can explain more parsimoniously why the effective reproduction number sometimes undergoes large fluctuations in the absence of behavioral changes.

Moreover, as I already noted, I am not claiming that population structure is the only factor explaining the dynamic of the epidemic. In particular, I don’t question that people’s behavior also matters a lot, so it’s not as if population structure had to explain everything on its own.30 I would expect population structure to matter relatively less for waves that are more synchronized across regions and relatively more for waves that are less synchronized across regions. Simulations show that, even if you assume that the subpopulations in each subnetwork are to a large extent concentrated in just one region, it’s easy to obtain the amount of synchronicity we observe in real data except for the most highly synchronized waves. For instance, here is a graph that shows what happens when I randomly distribute the subpopulations in the network used for the simulation I presented above into 15 regions, randomly assigning a region to each subnetwork and assuming that each subpopulation in that subnetwork has a probability of 2/3 to be in that region while the rest of the probability is distributed uniformly across the other regions:

As you can see, even when I assume that subnetworks are heavily concentrated in one region, we can still end up with something that looks a lot like the synchronicity we find in real data. Thus, I don’t think the objection based on how synchronized waves in real data are is very powerful, at least as long as we don’t claim that population structure is the only factor driving the dynamic of the epidemic.

Again, ultimately the hypothesis that population structure has been a significant factor driving the dynamic of the epidemic will remain conjectural until we get data that bear directly on it, which may never happen. In any case, as long as we don’t have such data, we have to consider how much explanatory power each alternative theory has. Now, not only can this theory explain the fact that the effective reproduction number often undergoes large fluctuations despite the apparent lack of behavioral changes better than standard epidemiological models, but this isn’t the only phenomenon it could help to explain. For instance, most people have been surprised that, even after the vast majority of their population has been vaccinated, many countries still experienced large outbreaks. The most striking example, though hardly the only one, is the large wave that started in England this summer and is still ongoing:

The prevalence of people with antibodies against SARS-CoV-2 in England at the end of June was estimated at 91.9% among people 16 and over. If we assume that 25% of people under 16 in England had been infected by that point and that everyone who tests positive for antibodies is immune, this implies a prevalence of immunity of approximately 79% in the population as a whole, which is well above the herd immunity threshold predicted by standard epidemiological models unless we assume a very high basic reproduction number.31 For instance, in the SIR model, the virus would need to have a basic reproduction number of more than 5 for a country where 79% of the population is immune. If you complexify the model a little by taking into account different age groups, but still assume that people in the same age group mix homogeneously, the basic reproduction number you have to assume is even higher.

It’s true that the Delta variant that was associated with the latest wave in England is widely believed to be more than twice as transmissible as the original strain, which probably implies a basic reproduction number greater than 6 in England, but as I argued at length elsewhere, Delta’s transmissibility advantage is probably vastly overestimated. Moreover, even if I’m wrong about that, the basic reproduction number in the sense that is relevant for this discussion is not a fixed quantity but depends on people’s behavior. Now, as you can see on this chart, mobility data show clearly that even now people in England still have not returned to their pre-pandemic behavior:

Thus, even if Delta were really twice as transmissible as the original strain, this presumably would translate into a basic reproduction number much smaller than estimates obtained by multiplying the basic reproduction number at the beginning of the pandemic by 2.32 For instance, if we assumed that Delta would have a basic reproduction number of 6 under the conditions that prevailed in England before the pandemic, the fact that people still haven’t returned to their pre-pandemic behavior would only need to reduce it by less than 15% for England to be above the herd immunity threshold this summer, which is hardly inconceivable.33 Of course, if I’m right that Delta’s transmissibility advantage has been significantly overestimated, it’s even harder to make sense of what happened in England within the traditional modeling framework.

Now, my argument so far has implicitly relied on the assumption that people who have recovered or have been vaccinated can’t be infected again, but the protection conferred by immunity, whether naturally acquired or induced by vaccination, is not perfect and it seems to wane over time, so this is not true. Standard epidemiological models can be modified to relax this assumption and, if you assume that vaccine efficacy wanes quickly enough, it’s possible to explain English data without assuming an implausibly high basic reproduction number. However, while I do not doubt that more transmissible variants and waning are part of the story here, I still think that, unless you model complex population structure, you have to make rather implausible assumptions to make sense of large outbreaks in places where the rate of people who have antibodies against SARS-CoV-2 is very high. Again, the point is not that models that make the homogeneous mixing assumption or something close to it can’t explain the data, which is trivially false because as I have already noted standard epidemiological models are remarkably flexible and it’s always possible to make them fit the data. The problem is that, in order to do so, you often have to make assumptions that are implausible. In the case of the assumptions you have to make to explain why places where the prevalence of immunity was very high nevertheless experienced large outbreaks, I don’t think it’s as clear-cut as when you have to assume massive behavioral changes even though mobility data don’t show any, but I still think that you have to make dubious assumptions. On the other hand, if the population has the kind of structure I have assumed in my simulations, then it’s not surprising that places where the prevalence of immunity is much higher than the herd immunity threshold predicted by standard epidemiological models can nevertheless experience large outbreaks, because that’s exactly what is going to happen if part of the networks that had been spared so far are seeded. To be clear, I do not doubt that more transmissible variants and waning are part of the story, I just think that population structure could be another part of it. In fact, just as the effect of behavioral changes on transmission can be mediated in part by the effect it has on the topology of the network on which the virus is spreading, the emergence of more transmissible variants and the waning of immunity can affect transmission not just directly but also through the effect they have on that topology.

Another phenomenon that is even harder to explain within the standard modeling framework, which I already discussed at length before, is the way in which Delta and before that Alpha replaced previously established lineages in most countries. The standard view is that both of them had a very large transmissibility advantage over previously established strains of the virus. In other words, other things being equal, people infected by Alpha cause more secondary infections than people infected by previously established variants and people infected by Delta cause more secondary infections than people infected by Alpha and the other variants that coexisted with it. The estimates of this transmissibility advantage vary wildly for both Alpha and Delta, but the estimate of 50% seems to have stuck in both cases for no particularly good reason that I can see, which is why people often say that Delta is more than twice as transmissible as the original strain of the virus. The problem with that standard view is that it can’t explain why both Alpha’s and Delta’s transmission advantages relative to previously established strains have been fluctuating wildly over time and space. For instance, here is a chart that shows Delta’s transmission advantage over previously established variants across French departments earlier this year, plotted against the prevalence of that lineage in each department during each period:

As you can see, not only is there a clear downward trend as the lineage becomes more prevalent, but at any point in time the estimates of Delta’s transmission advantage vary wildly across departments.

As I also noted at the time, the same thing happened before with Alpha, not just in France but also in the UK. In fact, if we look at Alpha’s and Delta’s transmission advantages in the UK, we also see them undergo wild fluctuations over both time and space:

On the standard view, it’s hard to see how this extreme variability of Alpha’s and Delta’s transmission advantages could be explained in a model that assumes the population is mixing homogeneously.34 You would have to assume that mysterious factors present in some places but not in others or during some periods but not others had a massive effect — much larger than Delta’s alleged transmissibility advantage or even than the ridiculously large effect that some studies ascribe to non-pharmaceutical interventions — on Delta’s transmission but not on the transmission of the other variants or the other way around.

On the other hand, as I explained in my post about Delta’s transmissibility advantage, there is nothing particularly surprising about this variability if the population is structured in networks that are internally well-connected but loosely connected to each other. The idea is that, if different variants don’t spread in the same networks and some of them spread in networks where the prevalence of immunity is low because they had been relatively spared so far, a variant’s transmission advantage over the other strains of the virus can significantly overestimate its transmissibility advantage. Indeed, in that case, it will spread much faster relative to other variants than it would have other things being equal, because it’s spreading in networks where the prevalence of immunity is lower than in the networks where other variants are spreading and things are therefore not equal. Thus, it’s crucial to distinguish a variant’s transmission advantage over another (i. e. how fast it’s actually spreading relative to it) from a variant’s transmissibility advantage over another (i. e. how fast it would spread relative to it other things being equal), because they can diverge radically in the presence of complex population structure. This could also explain why, in France, both Alpha’s and Delta’s transmission advantage collapsed after the initial phase of expansion. This is what you would expect if a new variant initially expanded in networks where the prevalence of immunity was relatively low, while the previously established variants had nearly exhausted the pool of susceptibles in the networks where they are spreading, because they have been circulating for longer. Moreover, because there is no reason to expect that subpopulations in each network are distributed uniformly across regions and, on the contrary, every reason to expect them to be heavily concentrated in one region, it’s also entirely unsurprising if the population is structured in that way that a variant’s transmission advantage varies wildly across regions.

At the time, I laid out the argument in purely intuitive terms, but now I can back it up with simulations. In order to show that one variant could easily have a very large transmission advantage over another without being intrinsically more transmissible, I used the same model as above, randomly generating a network of subpopulations in the same way. However, instead of seeding the network with the same variant for the whole duration of the simulation, I seeded it with one variant during the first 150 days and, starting on the 180th day, with another for the rest of the simulation. Crucially, I have assumed that both variants have exactly the same basic reproduction number in each subpopulation, so by assumption neither has any transmissibility advantage over the other. This figure shows the daily number of infections in that simulation, with infections for both variants summed in the upper panel and disaggregated in the lower panel:

As you can see, after the population is no longer seeded with the first variant, it continues to circulate for a while but after about 150 days it can’t find anyone susceptible in the networks where it was spreading anymore and dies out. Meanwhile, after the second is introduced into the population, it eventually reaches a network where the prevalence of immunity is low and starts new waves of infections.

If we compute the transmission advantage of the second variant over time, keeping only observations with at least 100 infections for each variant (in order to eliminate any large fluctuations that might occur at low incidence due to the stochastic nature of the transmission process), here is what it looks like:

As you can see, although by assumption both variants are equally transmissible, the second variant nevertheless has a very large transmission advantage that undergoes large fluctuations over time but trends downward.35 This demonstrates that, even if a variant has no transmissibility advantage whatsoever over another, it can still have a large transmission advantage over it because it’s spreading in networks where the prevalence of immunity is lower. Of course, as I explained in my post on Delta’s transmissibility advantage, I don’t claim that Alpha and Delta have no transmissibility advantage, but that it has been largely overestimated because people have been careless in inferring a transmissibility advantage from the observed transmission advantage, which as this simulation shows can easily diverge radically from the transmissibility advantage because populations don’t actually mix homogeneously.

I also computed the second variant’s transmission advantage separately in each region, after randomly assigning regions to subpopulations in the same way as before. In order to do that, I only kept observations with at least 25 infections for each variant and excluded regions in which that left less than 20 observations (this removed 3 regions out of 15), to avoid the extreme variability that can be caused by the stochastic process of transmission at very low incidence.36 As you can see, as in real data, we find even more variability than at the aggregate level:

Thus, not only can population structure explain why the effective reproduction number can undergo large fluctuations even in the absence of significant behavioral changes, but it can also make sense of the wild variability of Alpha’s and Delta’s transmission advantages, which standard epidemiological models that make the homogeneous mixing assumption can’t. The fact that epidemiologists have largely ignored this variability doesn’t negate this advantage of my theory, because they shouldn’t have ignored it and, if they have, it’s probably in large part precisely because it’s impossible to make sense of it within the traditional modeling framework. Again, this doesn’t prove that my theory is correct, but I think it’s enough to seriously consider the possibility that complex population structure of the sort I assume in my simulations plays a significant role in the real world and to ponder what implications it would have if that were true, which is what I turn to in the next section.

Have we been thinking about the dynamic of the pandemic in the wrong way all this time?

If real populations have the kind of structure my theory posits, then a lot of what people who study the pandemic have been doing is completely wrong. Thus, if I’m right that we should take that hypothesis seriously, it should at least make everyone nervous. First, since the beginning of the pandemic, we have been obsessed by quantities — the effective reproduction number and the herd immunity threshold — that are essentially meaningless at the aggregate level in a model with complex population structure. In the modeling framework I have used above, they make sense at the level of subpopulations, but at the aggregate level they are uninterpretable or misleading if we interpret them as if the virus were spreading in a homogeneous mixing population. As we have seen, not only can incidence fall even in the absence of behavioral changes when the prevalence of immunity is much lower than the herd immunity threshold predicted by a model with homogeneous mixing or something close enough (because the virus has exhausted the pool of susceptibles in one part of the network and wasn’t able to reach another part from there before this happened), but it can also rise when the prevalence of immunity is significantly above that threshold (because there are still parts of the network where most people do not have immunity). Similarly, while the effective reproduction number may be meaningful for parts of the network that can be idealized as homogeneous mixing populations (as I have done for my simulations), at the level of the population as a whole it just aggregates the dynamics of the epidemic in different parts of the network and doesn’t have the meaning that has been ascribed to it by everyone since the beginning of the pandemic. In particular, changes in the effective reproduction number at the aggregate level cannot be interpreted as a sign that people change their behavior in a way that affects transmission, that non-pharmaceutical interventions work or don’t work, etc. Yet this is what everyone has been doing for more than a year and a half and it’s what everyone is going to keep doing this winter.

The problem is not limited to journalists and public officials, who have spent the entire pandemic trying to read some kind of causal story into changes of the effective reproduction number, it also affects the scientific literature on the pandemic, which has been used to guide policy. Indeed, if the population has the kind of structure I have proposed, then not only are the methods used to estimate the impact of non-pharmaceutical interventions, behavior and even vaccination on transmission completely unreliable, but so are the projections based on the estimates that were obtained with those methods. As I have explained before, studies on the impact of non-pharmaceutical interventions can roughly be classified into 2 groups, depending on whether they assume a particular epidemiological model or use seemingly more agnostic econometric methods to estimate the effects of non-pharmaceutical interventions. The first type of study basically asks what effect non-pharmaceutical interventions must have had on transmission to explain the data if we assume they were generated by a standard epidemiological model. Thus, if the daily number of infections went down before the herd immunity threshold implied by the model was reached, this method will ascribe a large effect to whatever non-pharmaceutical interventions started around that time, because that’s the only way it can fit the data. But what if the data were not generated by a standard epidemiological model, with a homogeneous or quasi-homogeneous mixing population? In that case, this method may also find that non-pharmaceutical interventions had a very large effect, even if they only had a small effect or no effect whatsoever! In particular, if the population has the kind of structure I have assumed for my simulations, this method may conclude that non-pharmaceutical interventions have a very large effect even if they didn’t have any or only a small one. The most famous example of this type of study, which may also be the most cited paper during the pandemic (it has already been cited 1,662 times as I write this), is Flaxman et al. (2020), which I have already criticized in detail elsewhere. However, it’s hardly the only example, there are dozens and probably hundreds of others that use the same method.

In order to illustrate the problem with this method, I fitted a standard epidemiological model with homogeneous population mixing to the first 200 days of data (corresponding to the first wave) from the simulation with complex population structure and a single variant I presented above, but I told the model that a lockdown was in effect from the 105th day and that it wasn’t lifted until 2 months and a half later:

Of course, no lockdown whatsoever played any role in the data generating process, but the model doesn’t know that, so it tries to figure out what effect this non-existent lockdown must have had on transmission to fit the data as best it can on the assumption that the virus was spreading in a homogeneous mixing population.37 What it concludes is that the lockdown reduced transmission by more than 40%. Thus, although there was no lockdown and therefore its real effect was zero, using the same method that epidemiologists have used in countless studies since the beginning of the pandemic, I find that it had a very large effect. This is because the model wrongly assumes a homogeneous mixing population, so it assumes that herd immunity hasn’t been reached yet, but in fact it has been reached in the part of the network where the virus was spreading during the first wave. As a result, it ascribes this reduction of transmission to the lockdown (which didn’t even happen and therefore had no effect whatsoever), even though it was the effect of population structure. Thus, if the population has the kind of structure my theory posits, this method will be completely unreliable, yet dozens of studies have used it to estimate the impact of non-pharmaceutical interventions since the beginning of the pandemic.

The other type of studies that estimate the effects of non-pharmaceutical interventions use a more traditional econometric approach. Roughly, instead of assuming a particular epidemiological model that includes parameters for the effect of non-pharmaceutical interventions and fitting epidemic data to that model, they look for correlations between non-pharmaceutical interventions and the growth of the epidemic. On the surface, this approach seems more agnostic than the previous one, but this is largely an illusion. While this method doesn’t require that one explicitly make strong mechanistic assumptions about the data generating process, if the effects are to be interpreted causally, one still has to make strong assumptions about that process. While many papers using that approach keep those assumptions implicit, a paper by Chernozhukov et al. I criticized a few months ago actually spelled them out explicitly by using the SIR model to motivate their econometric model, which makes clear that it rests on the homogeneous mixing assumption.38 It’s actually not hard to understand intuitively why, if this assumption doesn’t hold, their model and similar econometric approaches will not be able to recover the causal effects of non-pharmaceutical interventions. As we have seen, in the presence of complex population structure, the effective reproduction number can undergo large fluctuations even without any behavioral changes. For instance, it can suddenly fall because the virus has exhausted most susceptibles in a part of the network, but failed to reach another part of the network with more susceptibles from there. Therefore, if a non-pharmaceutical intervention happened to be in place around the time this happened, there will be a correlation between that non-pharmaceutical intervention and the growth of the epidemic. This correlation will be interpreted as the causal effect of the non-pharmaceutical intervention, even if it didn’t have any causal effect on transmission. In theory, this could also bias the estimate of the effect of non-pharmaceutical interventions in the other direction and make one conclude that non-pharmaceutical interventions increase transmission, but in practice I think it’s unlikely since decision-makers typically order non-pharmaceutical interventions when incidence has reached a high enough level and tend to keep them in place for a relatively long time after it has started to go down.

We can also illustrate this point by fitting a simple version of the model used in Chernozhukov et al. (2021) to the same data I used above to show that the method used in Flaxman et al. (2020) was not reliable when the homogeneous mixing assumption doesn’t hold and the virus is spreading in a population that has strong community structure.39 This model leverages the variation of non-pharmaceutical interventions across time and regions to estimate the effect they have on the daily growth rate of infections by looking at how the presence or absence of non-pharmaceutical interventions is related to that variation.40 I randomly drew a date between the 100th and 140th day of the simulation in each region, told the model that a lockdown was in effect in that region for 60 days starting from that date and the model used that information plus the data on infections to estimate the effect of this non-existent lockdown. I repeated this procedure 1,000 times and here is the distribution of the estimates it found:

As you can see, according to the model and depending on when the lockdown was supposed to be in effect in each region, a lockdown that never took place and therefore had no effect whatsoever reduced the daily growth of infection by 7% to 10%. Not only is this a very large effect, but it was statistically significant at the conventional 0.05 level in every single case, which shows that the kind of model used in Chernozhukov et al. (2021) is completely unreliable in the presence of complex population structure of the sort that is assumed by the model used to generate the data.

This discussion illustrates a deep point, which most scientists understand but the public does not, namely that statistics can only help you to answer questions about the world by making assumptions about the world. If those assumptions are false, the answers it gives you cannot be trusted. For instance, in the case of the methods used above to estimate the effect of a lockdown, the model assumes that the virus spreads in a homogeneous mixing population. If that assumption is true or close enough to the truth, it may allow you to estimate the effect of a non-pharmaceutical intervention pretty accurately, but if that assumption is completely false, as is the case in the data I generated with a model that assumes the virus is spreading in a network of homogeneous mixing subpopulations that can be divided into subnetworks that are internally well-connected but only loosely connected to each other, then it will produce completely unreliable estimates, as we have just seen. Indeed, while it’s true that the effect of the lockdown is estimated from the data, it’s not estimated just from the data, because the estimation also relies on the assumptions that are made about the data generating process. This is always the case, because you can never estimate a causal effect just from the data and you always need to make assumptions about the world. Unfortunately, most people don’t realize that, so they think that the results of empirical studies can be taken at face value because the effects of such-and-such intervention was estimated “from the data”.

In the case of studies that estimated the effect of non-pharmaceutical interventions on transmission, homogeneous population mixing was usually assumed (regardless of whether the authors realized it and whether they realized that it was not a trivial assumption), so if I’m right that we have good reasons to think that real populations depart significantly from that assumption, we cannot trust their conclusions. Note that I’m not even saying their conclusions are false, although I think they are (as I have explained at length before there are other reasons to think so beside the fact that real populations are not mixing homogeneously), I’m just saying that we have no reason to be confident they are true because we have no reason to think the homogeneous mixing assumption on which they rest is close enough to the truth for the methods they use to be reliable, which is a much weaker claim. Even if that assumption is close enough to the truth, the fact that we don’t know that and that we even have good reasons to doubt it should result in a healthy dose of skepticism toward studies that implicitly rely on it, but unfortunately neither experts nor public officials have demonstrated much skepticism about their conclusions. In fact, they have used the results of those studies — which are sometimes comically bad even if you set aside the issue of the homogeneous mixing assumption — to make projections that were used to guide policy, which may be part of why those projections have systematically and massively failed since the beginning of the pandemic. If the population has the kind of structure posited by the theory I explored above, then it’s not surprising that projections were so unreliable. Indeed, if the virus spreads on a network that has that kind of community structure, then at best aggregate-level statistics can be used to forecast the short-run evolution of the epidemics (as some machine-learning techniques have been able to do with a measure of success), but any attempt to forecast the epidemic beyond that is pointless because there is no way to predict if or when the virus will reach another part of the network where it will find enough susceptibles to expand again.

Conclusion

I have argued that, while there are solid theoretical reasons to think that ultimately the dynamic of the epidemic depended on people’s behavior, there is also strong evidence that the effective reproduction number sometimes underwent large fluctuations that could not be explained by changes in people’s behavior. The cyclical nature of the epidemic has often been noted, but except for the vague claim that respiratory infections are “seasonal” (which is true but doesn’t actually explain much), nobody has really tried to explain it. In this post, I have proposed that population structure could be part of the explanation, because real populations are not homogeneous mixing. This theory can explain why, although ultimately transmission depends on people’s behavior, the effective reproduction number can undergo large fluctuations even in the absence of behavioral changes. While there is no evidence bearing directly on this hypothesis one way or the other, it can explain many phenomena that are difficult to explain with standard epidemiological models, which assume homogeneous mixing or something close to it. Of course, this doesn’t mean that other factors, such as behavioral changes but also more transmissible variants, vaccination and meteorological variables, don’t also play a role, which I’m sure they do, but I think that we should at least take the possibility that population structure plays a large role seriously. Indeed, even if this possibility turned out to be false, the fact that we have good reasons to believe it’s true should lead us to question how we have been thinking about the pandemic so far. If real populations are structured in the way my theory posits, not only are several quantities, such as the effective reproduction number, we have been obsessing over largely meaningless at the aggregate level, but the methods used in the literature to estimate the effect of non-pharmaceutical interventions, vaccinations, etc. could be totally unreliable. This suggests that we should build the capacity to collect data about the characteristics of the network on which infectious diseases spread, so that when the next pandemic hits, modeling can take into account population structure and therefore produce better projections and more reliable estimates of the impact of interventions.

Addendum on the relationship between the hypothesis discussed in this post and the earlier debate about the effect of heterogeneity in social activity

Based on the response to this post, many people seem to think what I’m saying is the same thing as what people who argued back in 2020 that heterogeneity in social activity might lower the herd immunity threshold, but while this is related to what I’m talking about here it’s actually different so I thought it might be useful to briefly explain why. I’m actually familiar with the debate that took place about that last year, since I even wrote a post about it at the time. In both cases, the point is that heterogeneity affects the dynamic of the epidemic, but it’s not the same kind of heterogeneity. What people were arguing last year is that, if people’s level of social activity varies a lot, herd immunity will be reached sooner because the people who spread the virus the most are also the most likely to be infected early in the pandemic.41 This intuitive argument is supported by models showing that, when you introduce that kind of heterogeneity, herd immunity does in fact occur sooner. If we model the spread of the virus on a network, this debate was mostly about the degree distribution, i. e. the distribution of the number of edges connected to each individual in the network. The point was that, when this distribution is more dispersed than standard epidemiological models implicitly assume, the herd immunity threshold will be lower than predicted by those models.

However, the kind of epidemic behavior I discuss in this post only arises when the network has community structure, which is about a lot more than the variance of the degree distribution.42 In particular, the network must exhibit a specific kind of clustering, but this doesn’t just depend on its degree distribution. In fact, it’s conceivable that at the level of the parts of the network that I idealized as homogeneous mixing population in my simulations, the herd immunity threshold is lower than predicted by standard epidemiological model due to heterogeneity in social activity, even though at the aggregate level it’s higher due to community structure, as I explained above. So while most people have interpreted the fact that many places with a high prevalence of immunity have recently experienced large outbreaks as proof that people who argued that heterogeneity in social activity could lower the herd immunity threshold were wrong, this is not actually the case if the network on which the virus is spreading has the kind of structure assumed in this post. Of course, like the rest of this post, this is very speculative, but it goes to show that the spread of infectious diseases is a lot more complicated than people generally assume.

Addendum on what I expect the import of population structure to be going forward

As I have explained before, the pandemic is on its way out and the virus is going to become endemic, though not every place is at the same stage of that transition. If I’m right that population structure has played a key role in the dynamic of the pandemic so far, what role should we expect it to play as the virus becomes endemic? I haven’t tried to model this, but it’s an interesting question, so I figured that it would be useful to add a few words about this. Basically, while I expect that population structure will continue to be relevant even after the virus has become endemic (because the population still won’t be homogeneous mixing), I also expect that it will become less relevant as we get closer to the endemic equilibrium and that seasonal effects due to meteorological variables will progressively become dominant. This is what I expect mainly for 2 reasons. First, as more and more people have been infected or vaccinated, the different parts of the network will become more homogeneous in terms of susceptibility to infection. Second, although the population will not magically become homogeneous mixing as the virus becomes endemic, I nevertheless expect that it will get closer to this idealization because once people go back to their regular behavior it will presumably increase connectivity between different parts of the graph. So eventually I think it will leave other factors, mainly seasonal effects due to the direct and indirect effects of meteorological variables but also the occasional emergence of new variants that are more transmissible or better able to evade prior immunity, will dominate the effect of population structure and the occurrence of waves will become more reliably predictable.

Summary

• The Delta variant, which was first detected in India in October and has recently been spreading very quickly in many regions of the world, is widely believed to be more than twice as transmissible as the original strain of the virus. This belief has generated widespread anxiety and led public health agencies in several countries to revise some of their recommendations.

• In this post, I start by explaining what people mean when they say that a variant is more transmissible than another, which leads me to make a distinction between a transmissibility advantage and a transmission advantage. While this distinction is rarely made explicitly, it is absolutely crucial to interpret the evidence correctly, as the rest of the post shows.

• I then present the evidence used to support the claim that Delta is more than twice as transmissible as the other variants and argue that, while it clearly shows that Delta had a substantial transmission advantage during its initial expansion in many places, this doesn't show that it has a transmissibility advantage, let alone that estimates of its transmission advantage during its initial expansion accurately estimate any transmissibility advantage it might have.

• In fact, by looking at French data beyond Delta's initial expansion, I show that, as it became the dominant strain in France, Delta's transmission advantage collapsed rapidly. This is the exact same thing that already happened a few months ago with Alpha and something that is hard to square with the hypothesis that it's more than twice as transmissible as the original strain of the virus. I also show that Delta's transmission advantage varies wildly across regions, which suggests that other factors besides whatever transmissibility advantage it might have explain why it initially had such a large transmission advantage.

• I explain why, if they continue to do the same thing, epidemiologists will eventually conclude that Omega or whatever they call the next variant of concern has a basic reproduction number of 125, at which point one hopes they will recognize the unreliability of their methods. Unfortunately, while the literature on Delta's transmissibility advantage is full of caveats that show they understand why the evidence must be interpreted carefully, most of them naively plug the estimates in that literature into the models they use to make projections, which has recently led to some spectacular failures.

• Finally, I propose a theory that can explain why Delta's transmission advantage was initially very high before collapsing, just as Alpha's before it. This theory crucially rests on the assumption that, unlike what most epidemiological models used during the pandemic assume, the population is highly structured. The effect of complex population structure on transmission has far-reaching implications beyond the debate about Delta's transmissibility advantage, which I will explore in a forthcoming blog post where I will present modeling work I have done on this question.

The Delta variant of SARS-CoV-2, first detected in India last October, has recently been spreading rapidly in many countries and is now the dominant variant of the virus in most of them. According to the American Society for Microbiology, it’s more than twice as transmissible as the original strain of the virus, while the CDC claimed it was as transmissible as chickenpox. As a result, the agency recently published new guidelines on masking, recommending that even vaccinated people wear masks indoors in communities with high transmission of the virus. While there is compelling evidence that vaccines work fine against Delta, such as this study based on data from England, many are concerned that Delta’s high transmissibility means that vaccination will not be sufficient to contain the virus and that non-pharmaceutical interventions such as masking or even lockdowns and curfews will be necessary again. But I think the consensus on Delta’s transmissibility is deeply flawed and I will explain why in this post. I will start by explaining how epidemiologists have reached the conclusion that Delta is more than twice as transmissible as the original strain of the virus and why the inference they’re making could easily be misleading. In doing so, I will clarify some conceptual issues that I think are important to interpret the evidence correctly, but haven’t received enough attention in this debate. I will then present evidence showing that in fact Delta isn’t as transmissible as epidemiologists and public health officials claim. Finally, I will argue that, by not taking into account that evidence and assuming that Delta is more than twice as transmissible as the original strain in the models they used to make projections, epidemiologists are providing misleading guidance to decision-makers that might lead them to implement suboptimal policies.

To read the rest, click here.

SARS-CoV-2 is going to become mostly harmless

You may have heard that, as they evolve, viruses necessarily become less lethal because it makes no evolutionary sense for them to kill the hosts on which they depend for their survival and reproduction, but this is a myth and it's not what I'm saying. The claim I'm making is based on a much sounder and more straightforward argument. But to understand why it's true, you first have to understand that, as the virologist Dylan H. Morris explained in a great essay, what made SARS-CoV-2 so dangerous is not so much its intrinsic characteristics but the fact that it was novel, which means that nobody in the population had immunity against it.1 Indeed, while the debate about whether SARS-CoV-2 was "worse than the flu" or "just like the flu" dominated the early phase of the pandemic and to some extent is still ongoing, this question is not even well-posed because there is no such thing as the dangerousness of a virus simpliciter. The dangerousness of a virus is always relative to a particular context. This should be obvious if you consider the impact that the availability of effective treatments can have on how much damage a virus does. For instance, HIV was initially devastating because it invariably killed the people it had infected within a few years after symptoms onset, but thanks to the development of effective treatments infected people can now live a relatively normal life, at least in the developed world where people can afford such treatments. HIV has not become any less intrinsically dangerous, but it's undoubtedly far less dangerous in societies where effective treatments are easily available.

In the case of SARS-CoV-2 though, the key contextual factor is what proportion of the population has immunity against it. Immediately after the emergence of the virus, the population was immunologically naive, which means that nobody had immunity against it beyond that conferred by the innate immune system against any pathogen.2 The amount of damage and disruption caused by a virus can differ wildly depending on whether the population in which it's introduced is immunologically naive to it. This is because, when nobody in the population has immunity, 1) the virus spreads more easily and infects more people because everyone is susceptible to infection and 2) when people get infected they have a much higher chance of developing a severe form of the disease because their immune system does not yet have any weapons specifically tailored to fight this virus. So the same virus, with exactly the same intrinsic properties, can do vastly more damage in a population that is immunologically naive than in a population where everyone has immunity against it, either because they have previously been infected or because they have been vaccinated. That's one of the reasons why entire indigenous communities in America were almost completely wiped out by pathogens brought by Europeans, even though people in Europe had been living with the same pathogens for centuries or even millennia and, while they were not by any means harmless to them, they didn't threaten their existence.3

As more people get infected by SARS-CoV-2 or vaccinated against it, the virus will become endemic and continue to circulate following a seasonal pattern (because immunity whether acquired naturally or through vaccination is not 100% effective against infection and wanes over time), but the number of people who end up at the hospital or dead because of it will gradually decrease until we reach a sort of equilibrium.4 In some places, especially in developed countries where the vast majority of the population has already been vaccinated, this process is already well under way and you can see it on a simple chart:

This is probably also true in other regions of the world, where infections usually played a bigger role than vaccination, and eventually it will be true everywhere, including in places such as Australia and New Zealand that have mostly been able to keep the virus out so far but won't be able to do it forever as the virus becomes endemic in the rest of the world. Obviously, it's preferable to build up immunity through vaccination rather than infections, but eventually everyone will get to the same point. The virus will become endemic and virtually everyone will have some immunity against it, at which point it will be relatively harmless and no longer cause the kind of damage we have seen during the pandemic. The whole process will take a few years, but again it's already well under way in some places and this is where everyone is headed, dreams of eradication notwithstanding.

In order to understand how this transition takes place and why the virus will be mostly harmless once it has become endemic and the population is no longer immunologically naive to it, I think it's useful to work through a simple numerical example, which doesn't purport to be a quantitatively accurate description of what is going to happen but can illustrate the process qualitatively and help people to grasp the underlying logic. Let's consider a population of 10 million with 3 million people between 0 and 18 years old, 4 million people between 19 and 59 people and 3 million people 60 and over. Suppose that in that population a virus kills 0.05% of the people between 0 and 18 years old it infects, 0.2% of the people between 19 and 59 and 1% of the people 60 and over. Let's also assume that, during the first year after it's introduced in the population (which is initially immunologically naive to it), 25% of the population is infected and this doesn't vary by age. In that case, we expect that during that year it will kill 25% * 3,000,000 * 0.05% = 375 people between 0 and 18 years old, 25% * 4,000,000 * 0.2% = 2,000 people between 19 and 59 years old and 25% * 3,000,000 * 1% = 7,500 people 60 and over died, for a total death toll of 9,875. That is a pretty sizable mortality, comparable to what many countries have seen during the first year of the COVID-19 pandemic, which given the assumptions I made should not come as a surprise to anyone.

Now let's consider the same virus but in another population of 10 million or in the same population at a subsequent date where, because of vaccination and infections, the prevalence of immunity is only 25% among people between 0 and 18 years old, but 100% in the rest of the population.5 Let's further assume that immunity is 80% effective against death and that effectiveness doesn't vary with age, but that it's not as effective against infection. Still, it offers some protection against infection, so the virus doesn't spread as much as in a population where there is no immunity whatsoever. Let's be more specific and assume that, over the course of a year, 15% of people between 0 and 18 years old, 10% of people between 19 and 59 years old and 5% of people 60 and over get infected.6 Finally, let's assume that 75% of the children who get infected had no prior immunity, while 100% of the adults who get infected had some immunity since we have assumed that except for children everyone had immunity. In that case, we expect that 15% * 3,000,000 * (75% * 0.05% + 25% * (1 - 80%) * 0.05%) = 180 people between 0 and 18 years old, 10% * 4,000,000 * (1 - 80%) * 0.2% = 160 people between 19 and 59 years old and 5% * 3,000,000 * (1 - 80%) * 1% = 300 people 60 and over died, for a total death toll of 640. That's only ~6.5% of the death toll in the immunologically naive population, yet by assumption the virus is exactly the same as before, but the population is no longer immunologically naive and this changes everything. For various reasons I won't get into here, reality is far more complicated than this simplistic model, but it's good enough to grasp the basic logic that governs the transition toward endemicity and get a pretty accurate idea of what is going to happen.7

Sooner or later, as a result of both infections and vaccination, virtually everyone will develop some immunity against SARS-CoV-2. This immunity will not always prevent infection, but even if someone who has been vaccinated or previously infected gets reinfected, they will typically develop only a mild form of the disease, because while still not perfect the protection against severe illness that immunity confers is better and doesn't wane as quickly as protection against infection. Even the protection against severe illness will likely wane after a while, but this won't really be a problem because, since immunity is much less effective against infection and new people are going to get born who are completely susceptible because they have never been infected yet and won't be vaccinated, the virus will continue to circulate so most people will be reinfected every few years. Most people see that as a bug, but in a way, it may actually be a feature. Indeed, those reinfections will typically be mild because immunity protects well against severe illness, but they will update immunity and therefore ensure that, the next time someone is infected, this reinfection is also mild. As long as the virus is not eradicated, which as we have seen is not going to happen, we don't want it to circulate too much, but we also don't want it to circulate too little. Otherwise, too much time may elapse between two infections in the same person, in which case even the protection against severe illness conferred by immunity may have waned by the time they get reinfected.

Eventually most people will have a primary infection when they're children, which is perfectly harmless and, together with subsequent infections, will protect them against severe illness later, when infection would be more dangerous if they didn't have any immunity. Since once people have immunity, infections are generally mild, most people likely won't even bother getting vaccinated because the probability of becoming seriously ill due to SARS-CoV-2 will be very small since 1) the risk of getting infected in the first place will be low because immunity still offers some protection against infection and the virus will circulate much less after it has become endemic and 2) even if they are infected they will typically be well protected against severe illness. Elderly people will be the exception because their immune system is compromised, so for them it will make sense to get a vaccine booster on a regular basis and I expect that it's what most of them will do, as they already do against the flu. Once it has become endemic, which again will take a few years or even decades for the transition to be fully over, SARS-CoV-2 will become just another respiratory virus and will never cause the damages it has just wrought on us again. At last, it will have become "just like the flu", except that it probably won't be as bad as the flu if only because immunity will be more effective and longer-lasting.8 This may have already happened in the past with a coronavirus after the 1889-1891 "Russian flu" pandemic, which some now believe to have actually been caused by the emergence of HCoV-OC43, another human coronavirus that is now endemic and causes the common cold. It's likely that SARS-CoV-2 will follow a similar path and end up being similarly harmless.

How I learned not to worry about variants and why you shouldn't either

I have argued that, although SARS-CoV-2 is not going anywhere and that it wouldn't be eradicated, things are looking up and that as the virus becomes endemic it would become mostly harmless. However, I know that presented with the optimistic picture I painted of what lays ahead of us, many people will react in disbelief because they think that emerging variants of the virus will get in the way of this quasi-idyllic scenario. Instead of seeing the wave of infections associated with the Delta variant as the last jolts of a pandemic on the way out as the transition toward endemicity takes place, they see it as a sign that, because new variants will keep emerging, we are going to be trapped in a never-ending cycle of waves of infections, each of them leaving scores of dead behind. Given that since the end of 2020 and the emergence of the Alpha variant in England, a wave of variantophobia has taken over the world, I can't blame you if you worry that something like that might be true, but if that's the case then I think you will feel much better after reading this section because the case against this variantophobia is very strong and we have every reason to believe that variants won't prevent the scenario I described above from unfolding. First, before I say anything else, just taking another look at the chart about what just happened in England above should already assuage your worries somewhat, but there is more so please just bear with me for a little longer and I promise that you won't regret it.

Variants are neither a new phenomenon nor something peculiar to SARS-CoV-2. Viruses constantly mutate and, as a result, variants of SARS-CoV-2 started to emerge long before the public became aware of that phenomenon a few months ago. While I do not doubt that mutations can result in different properties, as I have already explained previously, the picture is more complicated than what epidemiologists claim, especially when it comes to their claims about the advantage of transmissibility that, according to them, some variants enjoy. But the real concern people have about variants in the long-run is that they might evade pre-existing immunity, in which case we'd pretty much be back to square one. Indeed, the optimistic prediction I made about what is going to happen as the virus becomes endemic depends on the fact that, once everyone has acquired immunity against the virus, it will no longer kill a large number of people because immunity will ensure that it circulates less so fewer people will be infected and that even when someone is infected the infection will usually be mild. Obviously, if new variants emerge that can evade this immunity, this is not going to work and the pandemic will not end. But this is not going to happen and people who say otherwise are just talking nonsense.

In order to understand why, you must know a few things about how immunity works. Most people think of immunity as a black-or-white kind of thing: you either have it and you're completely protected against both infection and severe illness or you don't have it and you're not protected against either. However, that is not how it works, the reality is more complicated. Immunity has several layers and comes in degrees. I have already noted that immunity against SARS-CoV-2 offered better protection against severe illness than against infection, but it's even more complicated than that. For one thing, even if you have never been infected by SARS-CoV-2 and have not been vaccinated, it's not true that you have no immunity against it. You have some immunity against it because your innate immune system is capable of fighting off even pathogens that you have never encountered. If this were not true, everyone who is exposed to SARS-CoV-2 would have died, but almost everyone survives and the overwhelming majority of people only have mild symptoms or no symptoms at all. It's just that sometimes this innate immunity is not enough to clear the infection on its own before things get ugly, so it needs the adaptive immune system, which is responsible for mounting a more specific immune response to pathogens.

Unlike the innate immune system, which offers generic protection against pathogens, the adaptive immune system offers tailor-made protection against specific pathogens that it previously encountered. It relies mainly on two types of cells, B-cells and T-cells, that each play a different role, but in both cases they work by recognizing parts of proteins called epitopes expressed by the pathogen, which in the case of SARS-CoV-2 is a virus. B-cells have receptors that directly bind epitopes on the surface of the virus, then proliferate and create antibodies that can also bind those epitopes, which prevents the virus from infecting cells and helps other types of cells in the immune system to remove them. In the case of T-cells, on the other hand, recognition is a bit more indirect. Viral proteins are first broken up into short chains of amino acids called peptides inside cells that are called antigen-presenting cells (APCs).9 Those peptides are then bound to molecules known as the major histocompatibility complex (MHC) and the resulting MHC-peptides complexes are transported to the surface of the APCs where they are presented for recognition by T-cells.10 T-cells have receptors that bind different types of MHC-peptide complexes and, if they recognize one of them, they get activated and start going to work against the virus. This contributes to the immune response in various ways, but in particular sets in motion the process that will result in the destruction of the cells that have been infected by the virus.11 Here is a chart adapted from this paper that summarizes B-cell and T-cell epitope recognition:

A key fact about both T-cells and B-cells is that, when they are activated, they don't just set in motion a process that will help clear the infection currently ongoing, but also a process that will allow them to do that more quickly the next time they encounter the virus.

You're probably wondering why I'm telling you about all that, but don't worry, you're about to find out. In the case of SARS-CoV-2, antibodies seem to be crucial to protect against infection, which makes sense because if there are still many antibodies that can neutralize the virus around when someone is exposed to the virus again, it won't even have the opportunity to infect cells and replicate. However, several studies have found that the number of antibodies against SARS-CoV-2 wanes relatively quickly after vaccination or a natural infection, so often immunity can't prevent infection. But as we have just seen, the immune response is not limited to antibodies, let alone to the antibodies against SARS-CoV-2 that are still around by the time someone is exposed to the virus again. Upon a second exposure with the virus, T-cells whose receptors bind peptides from SARS-CoV-2 will go to work again, but this time they'll be able to do it more quickly. This will ensure that, even if infection couldn't be prevented, it will be cleared before things take a turn for the worst. Thus, T-cells play a key role in preventing severe illness and, unlike antibodies, neither B-cells nor T-cells specific to SARS-CoV-2 seem to wane quickly. In fact, according to various studies (including one which found that T-cells specific to SARS-CoV-1 were still present in the blood of people who had been infected 17 years ago), they likely stick around for years. So even though protection against infection seems relatively short, immunity likely confers protection against severe illness for a long time. But won't new variants find a way to evade this pre-existing immunity and make even the protection against severe illness it confers ineffective? No, they almost certainly won't, and T-cells are the reason why.

Indeed, T-cells mount a particularly robust immune response because they target a much greater number of epitopes than antibodies, so even the virus mutates to prevent antibodies resulting from a previous infection to bind it, this is unlikely to work against T-cells because the entire viral proteome of the virus, i. e. the complete set of proteins expressed by the virus, would have to be different. But SARS-CoV-2 mutates pretty slowly, so although new variants regularly emerge and will continue to do so in the future, most peptides from the virus will remain the same and therefore T-cells will still be able to recognize them. Indeed, the peptides that are bound to MHC molecules and presented on the surface of antigen-presenting cells are very short chains of between 8 and 25 amino acids (depending on the class of MHC to which they are bound), so they are unlikely to change even as the virus mutates. Since it mutates slowly, it's kind of as if the virus were trying to win the lottery by just buying a handful of tickets, each of them with a very low probability of winning the jackpot. If it bought 500 of them, the probability that one of them is a winning ticket may be reasonably high, but since it only buys 8 to 25 of them in each case it's very low. Moreover, even if one amino acid changes, this is usually not enough to prevent T-cell receptors from binding, so in this case having a winning ticket does not even guarantee that the virus will actually pocket any money. Of course, it will sometimes happen, but T-cells target hundreds of epitopes from SARS-CoV-2, so it won't really make a difference to the overall immune response they mount against the virus. T-cells just take the recommendation that you shouldn't put all your eggs in the same basket very seriously.

This looks fine in theory, but reality has a way of frustrating our theoretical expectations, so does it also work in practice? Yes, it does, it works exactly as theory predicts. A recent study examined the impact of SARS-CoV-2 variants on T-cell reactivity and found that, depending on the type of receptor, between 93% and 97% of the hundreds of previously identified T-cell epitopes were not affected by mutations in the variants of concern. Now, all epitopes do not contribute equally to the immune response mounted by T-cells, so in theory it could be that while only a handful of them were affected by mutations in variants of concern, they happened to be epitopes that were disproportionately involved in the T-cell response. But the authors checked and found that fully conserved epitopes accounted for on average 91.5% of the response, so this isn't the case. Again, keep in mind that even for the handful of epitopes that were affected by mutations, it doesn't mean that receptors from a previous infection are no longer capable of recognizing them. In any case, the study also found there was no statistically difference in reactivity of T-cells from people who had acquired immunity against the virus, whether it was through vaccination or a natural infection. It doesn't mean that, had the sample been larger, a statistically significant difference wouldn't have been found, but it means that at worse the loss of reactivity was small and possibly non-existent, which again is exactly what we'd expect based on the theoretical considerations. It may be that, although T-cells target hundreds of epitopes and SARS-CoV-2 is mutating slowly, after a long enough period of time it will have mutated enough that T-cells won't be able to mount a strong enough immune response to protect against severe illness. But remember that SARS-CoV-2 is going to continue to circulate and that people will likely get reinfected every few years, so their immunity will be updated when they are, ensuring that any subsequent infections will also be mild.

But there is another reason almost nobody is talking about why it's unlikely that we'll see substantial immune evasion with T-cells. As I explained above, T-cells don't recognize epitopes directly on the surface of the virus, but rather bind complexes formed by MHC molecules and peptides on the surface of antigen-presenting cells. Now, different MHC molecules can bind different peptides, which are then presented for recognition to T-cell receptors. As it happens, the region of the human genome that is responsible for the production of MHC molecules is the most polymorphic in the entire human genome, which means that even in the same population different individuals usually have different MHC molecules that can bind different epitopes from the virus before presenting them to T-cell receptors on the surface of antigen-presenting cells. This fact has been confirmed in the case of SARS-CoV-2 by another study that identified potential T-cell epitopes from the virus and used computational methods to predict their binding affinity with the MHC molecules produced by the different variants of the genes that code for them in human populations. The authors found there was significant variation in the epitopes derived from SARS-CoV-2 involved in T-cell response both across individual within the same population and between populations, although this variation wasn't predicted to affect the overall level of response across individuals or populations.12 This is very important because it means that, even if the virus acquired mutations that allowed it to evade T-cell immunity in one individual or population, it typically wouldn't help it evade T-cell immunity in another individual or population, which makes T-cell immune evasion even more unlikely.

The bottom line is that, if you're the virus, T-cells are your worst nightmare. Getting ahead of antibodies is pretty easy and some variants of concern already do it to some extent, but T-cells are a completely different story and will be a much tougher nut to crack for the virus. As we have seen, we have very good theoretical and empirical reasons to expect that, in the war between the virus and T-cell immunity, not only is the latter going to win but it won't even break a sweat doing it. It's important to understand that, in that respect, SARS-CoV-2 is no different than other viruses and other viruses also have a hard time dealing with T-cell immunity. Indeed, as the authors of the study that examined the impact of SARS-CoV-2 variants on T-cell reactivity note, immune evasion at the level of T-cell response has never been reported for acute respiratory infections. People worry about variants because they hear that antibody response is not as effective against them, so they imagine that eventually another variant will emerge against which immunity will be completely ineffective, but that's because they don't know that antibodies are just one part of the immune response against SARS-CoV-2. Immunity has another layer depending on T-cells and, not only has this layer remained unaffected by mutations of the virus so far, but as we have just seen we have very good reasons to think it will continue to be true in the future.

As I noted above, it's likely that SARS-CoV-2 will follow a trajectory similar to that of the other human coronaviruses (which are already endemic), so it's particularly interesting to know that what I'm predicting for SARS-CoV-2 is exactly what is already happening with those human coronaviruses. A recent study examined the recent evolution of HCoV-229E, one of the four human coronaviruses that are already endemic, and found that its spike, the protein that allows the virus to enter cells and infect them, had undergone several mutations between 1984 and 2020. They used sera collected on recovering patients at various points during that period to test how well the antibodies they contain were able to bind reconstructed spikes of the virus from 1984, 1992, 2001, 2008 and 2016. What they found is that antibodies in sera collected at one date were able to find effectively the spikes that were found on HCoV-229E before that date, but not or not very effectively the spikes that were found on the virus after that date, which shows that HCoV-229E had mutated to evade antibody binding, which is already what we're seeing in SARS-CoV-2. But HCoV-229E remained mostly harmless during that period, which is presumably because while people's antibody response against it became less efficient due to mutations in the spike, T-cell immunity remained largely unaffected. This is exactly what we're seeing with SARS-CoV-2 so far and we have every reason to believe that it will continue to be true in the future. The only difference is that, in the case of HCoV-229E, nobody bothers naming the variants and people aren't freaking out because they think immunity will stop working against them. Again, SARS-CoV-2 is just another respiratory virus, what made it so devastating is that it was novel.

SARS-CoV-2 is not going anywhere

Some people insist that we can't "live with the virus" and that we must therefore pursue a policy of eradication. They often draw a parallel with smallpox and say that we should do the same thing with SARS-CoV-2 that we did with that virus, which after plaguing mankind for thousands of years was finally eradicated in 1980. This parallel is extremely misleading though, because smallpox differs from SARS-CoV-2 in very important ways, which made eradication possible though difficult in the case of the former but make it very unlikely in the case of the latter. Before I get into that, it's worth noting that to date only two infectious diseases have ever been successfully eradicated (smallpox in humans and rinderpest in cattle), which speaks to how difficult this sort of enterprise is. This is not for lack of trying, as several other infectious diseases have been targeted for eradication, but those efforts have not succeeded yet. Polio seems on the verge of eradication and probably will be eradicated soon, but isn't yet. Even in the case of smallpox, eradication took decades. You might take this to suggest that, while SARS-CoV-2 will not be eradicated overnight, we might pull it off eventually if we really commit to it. But I don't think it's going to happen because again SARS-CoV-2 is very different from the viruses that cause smallpox or polio.

First, while I think there is no doubt that vaccines against SARS-CoV-2 protect against infections and not just severe disease (as we have seen above), I think it's equally clear that the protection it offers against infection is far from perfect and that people can get infected even if they have been vaccinated. There is also growing evidence that, while it does not disappear almost immediately as some people had initially suggested based on weak evidence, the protection against infection conferred by vaccination is waning relatively quickly. As this study showed, the same thing is true for the immunity against endemic human coronaviruses induced by natural infection, so this is not particularly surprising. According to the COVID-19 Infection Survey, based on a random sample of the population in the United Kingdom, more than 90% of people had antibodies against SARS-CoV-2 in June, but it didn't prevent a gigantic third or fourth wave (depending on how you're counting) from ripping through the country in July. The same thing just happened in Iceland, where more than 90% of the population over 16 has received at least one dose of vaccine. As we have seen, this is not really a problem because thanks to vaccination and naturally acquired immunity mortality remained low, but it suggests that even mass vaccination within a short period of time cannot stop the virus from circulating. The vaccine against smallpox, on the other hand, probably confers lifelong protection against infection and the same thing seems to be true about naturally acquired immunity. Basically, in order to get rid of smallpox, we "just" needed to vaccinate everyone in their childhood and that was it. The same thing is true with polio.

So this means that, in order to eradicate SARS-CoV-2, we'd have to vaccinate the entire population every year for several years in a row and even that would probably not be enough.13 That's a much larger effort than what we had to do to get rid of smallpox, yet even that comparatively simple endeavor took decades. Who can seriously believe that we'll be able to sustain that effort for the years or even decades that it would take to eradicate the virus, when we aren't even able to do it in the middle of a pandemic that just killed millions of people? This is a pipe dream, it will never happen. Indeed, convincing or coercing people to get vaccinated is going to become even harder, because as I have explained the virus will be mostly harmless once it has become endemic. If you think it's hard to convince people to get vaccinated or politically difficult to coerce them to do so while people are dropping dead by the thousands, which it most certainly is, wait until the mortality caused by SARS-CoV-2 is divided by a factor of 20 or something. It's pointless and wasteful to pursue a policy that has no realistic chance of succeeding, but that's exactly what people who are calling to eradicate SARS-CoV-2 are doing. Not that it will make any difference, to be clear, because the same reasons that make this project a fantasy will ensure that calls to carry it out will remain unanswered.

Again the comparison with smallpox or even polio is extremely misleading here. Smallpox is one of the most lethal pathogens in history and has probably killed hundreds of millions of people in the last 100 years of its existence alone. It's painfully obvious that the incentives are completely different in the case of SARS-CoV-2. Even with polio, whose infection fatality rate is similar to SARS-CoV-2, the incentives are very different because it mostly kills or maims children. Does anyone really expect that people are going to be as motivated to eradicate a virus that mostly kills elderly people as they are to get rid of a virus that kills or paralyzes children? Moreover, as I already noted, in the case of polio, you just have to administer a few shots to people when they're very young children and you're done with it. The comparison of SARS-CoV-2 with other pathogens can be illuminating in some cases, but comparing it to smallpox or even polio to suggest that we could eradicate it and that it's a realistic possibility is extremely misleading. Even if we granted for the sake of the argument that it could be done if we committed enough resources to the effort, it's totally unrealistic to expect that we ever will, because the incentives aren't right.14

There are other differences between SARS-CoV-2 and smallpox or even polio that make it far more difficult to eradicate the former. In particular, smallpox and polio only infect humans, but SARS-CoV-2 can also infect animals and frequently does. While the evidence of animal-to-human transmission is so far very limited, I think it's mostly because the studies that have found evidence that animals could be infected by SARS-CoV-2 were not designed to answer that question. If the virus becomes endemic in some animal populations that are frequently in contact with humans, then even if we somehow managed to temporarily eradicate it from human populations, animals would just reintroduce it and we'd be back to square one. At least one animal reservoir has already been found in the white-tailed deer population in the US, so this isn't a purely theoretical worry. What this means is that, in order to permanently eradicate SARS-CoV-2 from human populations, we'd probably have to vaccinate wild animals. This can be done and has been done in some countries such as France, where a program to vaccinate some wild animals against rabies was undertaken, but it just makes eradication even more difficult and costly, which in turn makes it even more unlikely that we'll even try, let alone succeed.

Conclusion

The pandemic is on its way out, but SARS-CoV-2 is here to stay. Fortunately, as everyone develops immunity to it (whether through vaccination or natural infection), it will soon no longer be a major problem anymore. The virus will continue to circulate, but much less than during the pandemic and, even when people are infected, the infection will typically be mil

d. In the future, almost everyone will get infected for the first time during their childhood, which is harmless and will protect them against severe illness when they are reinfected.15 The virus will continue to mutate and some of those mutations will favor immune evasion, but while this will allow it to infect people who have already been infected or vaccinated more easily, immunity should continue to protect against severe forms of the disease, thanks in particular to the role played by T-cells. This is likely what happened with other human coronaviruses, which are already endemic and typically cause a cold in the people they infect. To the extent that immune evasion occurs, it will be very gradual and the fact that most people will be infected every few years will update their immunity, ensuring that subsequent reinfections will also be mild. The most vulnerable people, whose immune system doesn't work very well and could use some help to be ready in case of infection, can get a vaccine booster from time to time. The virus will still kill people, as the flu does, but it will never cause the same amount of disruption again. The hardest part of what lays ahead may be to convince people who have been traumatized by the pandemic that it's over and that restrictions are no longer necessary.

P. S. I realize that, while it doesn't exactly say that, this post makes it sound as though the only reason why protection against infection appears to have been waning is that new variants with mutations in the spike that allow them to prevent antibodies from binding have emerged, so to be clear that's not what I'm saying. I was focusing on immune evasion, because that's what people seem most worried about, but another reason why protection against infection is probably waning is that antibody levels progressively fall after infection. Moreover, as someone pointed out to me, so does the number of T-cells specialized against SARS-CoV-2 and I'm sure the same thing is true with B-cells, so as time goes by it also takes longer for the adaptive immune system to mount a response upon exposure to the virus. I also didn't mean to suggest that mutations in the spike make antibodies completely inefficient. The point I wanted to make is just that, even if a variant is able to evade humoral immunity to a large extent, T-cell immunity should still work just fine against it and eventually the immune system should be able to mount a very effective response to infection, even if the fact that T-cell levels also wane means that it will take longer as the time since the last infection increases.

Summary

• The effects of non-pharmaceutical interventions on the COVID-19 pandemic are very difficult to evaluate. In particular, most studies on the issue fail to adequately take into account the fact that people voluntarily change their behavior in response to changes in epidemic conditions, which can reduce transmission independently of non-pharmaceutical interventions and confound the effect of non-pharmaceutical interventions.

• Chernozhukov et al. (2021) is unusually mindful of this problem and the authors tried to control for the effect of voluntary behavioral changes. They found that, even when you take that into account, non-pharmaceutical interventions led to a substantial reduction in cases and deaths during the first wave in the US.

• However, their conclusions rest on dubious assumptions, and are very sensitive to reasonable changes in the specification of the model. When the same analysis is performed on a broad range of plausible specifications of the model, none of the effects are robust. This is true even for their headline result about the effect of mandating face masks for employees of public-facing businesses.

• Another reason to regard even this result as dubious is that, when the same analysis is performed to evaluate the effect of mandating face masks for everyone and not just employees of public-facing businesses, the effect totally disappears and is even positive in many specifications. The authors collected data on this broader policy, so they could have performed this analysis in the paper, but they failed to do so despite speculating in the paper that mandating face masks for everyone could have a much larger effect than just mandating them for employees.

• This suggests that something is wrong with the kind of model Chernozhukov et al. used to evaluate the effects of non-pharmaceutical interventions. In order to investigate this issue, I fit a much simpler version of this model on simulated data and find that, even in very favorable conditions, the model performs extremely poorly. I also show with placebo tests that it can easily find spurious effects. This is a problem not just for this particular study, but for any study that relies on that kind of model to study the effects of non-pharmaceutical interventions.

In the debate about lockdowns and other restrictions to slow down SARS-CoV-2’s spread, people on both sides like to cite studies that support their position. Indeed, whether you’re in favor of stringent restrictions or opposed to them, there is no shortage of studies that you can use to claim that your position is vindicated by science. To be sure, you mostly hear about pro-lockdown studies in the media, because journalists tend to be pro-lockdown, but there are plenty of studies whose conclusions vindicate the anti-lockdown side of the debate. As I explained in my case against lockdowns, most studies about the effect of non-pharmaceutical interventions fall roughly into 2 categories. First, you have studies that fit an epidemiological model, typically a compartmental model of some kind, on epidemic data. Non-pharmaceutical interventions are assumed by the model to affect transmission in a certain way and their effect is estimated by fitting the model on actual epidemic data. The other type of studies use econometric methods to estimate the association between non-pharmaceutical interventions and the growth rate of the epidemic or some related quantity such as R. They basically try to determine whether the epidemic grows more slowly when non-pharmaceutical interventions are in place.

The fundamental problem with the first kind of study is that, in order to use that approach, one has to make very strong mechanistic assumptions that at best one is not in a position to make and at worst are known to be false. Indeed, studies that fall in that category almost systematically assume that, until the herd immunity threshold is reached, only government interventions affect transmission, which is clearly false. If that were true, in the absence of government interventions, the epidemic would continue to grow until the herd immunity threshold is reached, at which point incidence would start to fall. But we have seen over and over that, even when R is much higher than 1 and the government doesn’t do anything more than it’s already doing, incidence peaks long before the herd immunity threshold is reached. There are several possible explanations for this phenomenon, which are usually not mutually exclusive, but my favorite is that, even in the absence of government interventions, people change their behavior in a way that reduces transmission when incidence starts blowing up. Of course, I’m not saying that people check incidence curves and adjust their behavior when they start climbing, but that people respond to various signals — the news is suddenly full of reports about hospitals filling up, people start hearing about friends and acquaintances who have been infected, etc. — that are correlated with rising incidence.

To read the rest, click here.

Summary

• B.1.1.7, a variant of SARS-CoV-2 that emerged in England last year and has been spreading rapidly everywhere since the beginning of the year, is claimed to be far more transmissible than the historical lineage. For instance, based on the early expansion of B.1.1.7 in France, Gaymard et al. (2021) found that it was between 50% and 70% more transmissible, which was used to recommend more stringent restrictions since if that were accurate a massive surge of incidence would be inevitable unless transmission were significantly reduced.

• However, this estimate is based on fitting a simple exponential growth model to 2 data points in January and is extremely sensitive to the assumptions made about the generation time distribution, about which I argue there is considerable uncertainty. When I replicate Gaymard et al.’s analysis but properly take into account this uncertainty by trying a wider range of possible assumptions about the generation time distribution, which I was able to do no thanks to them since not only did they not publish their code but they also didn’t reply when I asked them for it, I find that B.1.1.7 could be anywhere between 21% and 72% more transmissible, a much wider range than what is reported by Gaymard et al.

• If I fit the same type of model but use more recent data instead of relying only on the growth rate of B.1.1.7 in January, I find that B.1.1.7’s transmissibility advantage ranges from 16% to 42% depending on what assumptions I make about the generation time distribution, which is much lower than Gaymard et al.’s 50%-70% range. However, this conclusion is based on the assumption that B.1.1.7 has been growing exponentially in France since the beginning of the year, a view that is clearly falsified by the data even though some epidemiologists inexplicably continue to hold it.

• Most epidemiologists probably realize that, but argue that the explosion they predicted in January fail to materialize thanks to the decision to advance the curfew from 8pm to 6pm in January and the school holidays in February. So rather than assume a simple exponential growth model, I try to model the effect of government interventions and school holidays on transmission in a way similar to what the epidemiologists who advise the French government are doing, except that I use that model to estimate B.1.1.7’s transmissibility advantage instead of assuming it’s between 50% and 70% more transmissible. This approach leads to the conclusion that, depending on what assumptions we make about the generation time distribution, B.1.1.7’s transmissibility is somewhere between 22% and 53% more transmissible.

• I explain that, even if B.1.1.7’s transmissibility advantage had remained constant (which this approach implicitly assumes), this estimate would not be reliable because, as I argue elsewhere, this kind of model rests on strong and totally unrealistic mechanistic assumptions. So I also try an econometric approach to estimate B.1.1.7’s transmissibility advantage, which also assumes that it has remained constant, but is agnostic on the underlying mechanism. However, the estimates are even more all over the place than with the previous approach, with B.1.1.7’s transmissibility advantage ranging from -12% to 98% depending on what model I use and what assumptions I make about the generation time distribution.

• Thus, even if we assume, as epidemiologists systematically do (but rarely acknowledge explicitly), that B.1.1.7’s transmissibility advantage has remained constant, Gaymard et al.’s claim that it’s 50% to 70% more transmissible is completely unwarranted, since there is far more uncertainty than that. However, I show that B.1.1.7’s transmissibility advantage has not remained constant in France since the beginning of the year, but has rapidly fallen as this lineage rose in prevalence and I estimate that it’s now only 11% more transmissible than the historical lineage.

• Unfortunately, epidemiologists apparently couldn’t be bothered to check that B.1.1.7’s transmissibility advantage has remained constant, they just assumed it was and plugged Gaymard et al.’s 50% to 70% estimate into the models they use to make their projections, which unsurprisingly predicted that incidence would soon blow up like never before. Of course, this didn’t happen, but instead of admitting they were wrong and revising their assumption that B.1.1.7’s transmissibility advantage has remained constant, they just offered ad hoc rationalizations for why the projections didn’t come true even though they were right and continued to advocate for stringent restrictions.

The number of COVID-19 cases has recently started to increase again in several countries on both sides of the Atlantic. If you listen to epidemiologists in the media, the culprit is B.1.1.7, a variant of SARS-CoV-2 that first appeared in the UK and which they claim is far more transmissible than the historical lineage. Since it has rapidly expanded everywhere it’s been introduced, there is no doubt that B.1.1.7 is more transmissible or at least that it initially was. But how much more? Depending on the study, epidemiologists give various ranges of estimates, but B.1.1.7’s transmissibility advantage is always estimated to be very high. For instance, according to this study based on British data, this advantage is estimated to be somewhere between 43% and 90%. In this post, I will focus on Gaymard et al. (2021), another recent study based on French data that puts B.1.1.7’s transmissibility advantage between 50% and 70%, with a central estimate at 59%. Moreover, epidemiologists don’t merely claim that B.1.1.7 is far more transmissible than the historical lineage, they claim that this transmissibility advantage is constant.

They don’t just make those claims in scientific publications, but also in the media, where they often don’t show any caution about their estimates. For instance, after that French study was published, one of the co-authors, who also happens to sit on the scientific council that advises the French government on the pandemic, gave an interview to Le Monde, in which one would be hard pressed to find any trace of doubt about the validity of their estimates. It is thus unsurprising that journalists and commentators talk about the hypothesis that B.1.1.7 has a constant transmissibility advantage in that range as if this were established fact. However, not only is this hypothesis not established fact, but I think at this point it’s overwhelmingly unlikely to be true. Unfortunately, most epidemiologists don’t seem very interested in discussing the data that are hard to reconcile with that hypothesis, so in this post I will take a closer look at Gaymard et al. (2021) to explain how they concluded that B.1.1.7 was 50% to 70% more transmissible than the historical lineage and show that it’s not very serious.

To read the rest, click here.

• A year ago, when the COVID-19 pandemic hit most of the world, there was arguably a good case for lockdowns. The initial growth of the epidemic implied a high basic reproduction number, which in turn meant that unless transmission was reduced the virus would quickly sweep through most of the population because incidence would continue to grow exponentially until the herd immunity threshold was reached, overwhelming hospitals and resulting in the deaths of millions of people in a few weeks. Lockdowns and other stringent restrictions seemed like a plausible way of reducing transmission to "flatten the curve" and prevent that scenario from materializing.

• Many people continue to reason along those lines, but since then we have learned that, whatever the precise effect that lockdowns and other stringent restrictions have, it is not so large that it can easily be picked up in the data, as it would surely be if restrictions had the very large effect that pro-lockdown advocates claim. In particular, it is not the case that the alternative to lockdowns is herd immunity (at least in the short run), because in practice incidence never grows exponentially for very long even in the absence of stringent restrictions. While it is plausible that, without stringent restrictions, incidence would start falling a bit sooner and faster, the data show very clearly that it always starts falling long before the herd immunity threshold is reached with or without a lockdown.

• Many factors likely contribute, but the main explanation of that fact is probably that, despite what simple epidemiological models assume, people modify their behavior in response to changes in epidemic conditions such as rising hospitalizations and deaths, which reduces transmission and causes the epidemic to recede long before the herd immunity threshold is reached. However, until enough people have acquired immunity through natural infection or vaccination, this is only temporary and eventually incidence starts growing again because people go back to more regular behavior. Lockdowns and other stringent restrictions do not have a very large effect because they are a blunt instrument and have a hard time targeting the behaviors that contribute most to transmission.

• The belief that lockdowns are very effective nevertheless persists because authorities react to the same changes in epidemic conditions as the population, so they tend to implement lockdowns and other stringent restrictions around the time when people start modifying their behavior. This means that the effect of voluntary behavioral changes is attributed to lockdowns even if the epidemic would have started to recede in the absence of stringent restrictions. We know this because that is exactly what happened in places where the authorities did not put in place such restrictions, which are extremely diverse economically, culturally and geographically and therefore unlikely to share some characteristics that allow them to reduce transmission without a lockdown.

• Places where the virus seems to have spread more are those where the population is relatively young, which is exactly what the theory presented here–that voluntary behavioral changes in response to changes in epidemic conditions are the main driver of the epidemic–predicts, since a younger population implies a lower rate of hospitalization and death, which in turn means that the virus will have time to spread more before the rise in hospitalizations and deaths scare people into changing their behavior enough to push the reproduction number below 1.

• The scientific literature on the effect of restrictions on transmission contains many inconsistent results, but more importantly it is methodologically weak and therefore completely unreliable. To be sure, many studies found that restrictions had a very large effect on transmission, which pro-lockdown advocates like to cite. However, those results do not pass a basic smell test since one just has to eyeball a few graphs to convince oneself the studies they come from perform terribly out of sample, which is not surprising since most of them either assume that voluntary behavior has no effect whatsoever on transmission or do not use methods that can establish causality by disentangling the effect of restrictions from that of voluntary behavior changes.

• Even if you make completely implausible assumptions about the effect of restrictions on transmission, and ignore all their costs except their immediate effect on people's well-being, they do not pass a cost-benefit test. For instance, in the case of Sweden (where incidence is growing again and the government is considering tightening restrictions), if you assume that a lockdown would save 5,000 lives (which is approximately the total number of deaths during the first wave, when the population was behaviorally naive and vaccination was not under way), a 2-month lockdown followed by a gradual reopening over the next 2 months would have to reduce people's well-being by at most ~1.1% on average over the next 4 months in order to pass a cost-benefit. In other words, for a lockdown to pass a cost-benefit test under those assumptions, you would have to assume that on average people in Sweden would not be willing to sacrifice more than ~32 hours in the next 4 months to continue to live the semi-normal life they currently enjoy instead of being locked down.

• While I use Sweden to illustrate my point because it has been a focal point of the debate about restrictions, this exercise yields a similar conclusion almost everywhere else. The truth is that, from a cost-benefit perspective, Sweden's much-decried strategy has been vastly superior to what most Western countries have done and it is not even close. Even if you think that it would have been better for Europe and the US to follow Australia and New Zealand's example by adopting a so-called "zero COVID" strategy after the first wave, which would probably not have succeeded anyway even back then, this boat has already sailed and trying to pull it off now makes absolutely no sense from a cost-benefit perspective. Despite popular but confused arguments to the contrary, which I discuss at the end of this essay, this remains true even if you take into account the threat posed by new variants of SARS-CoV-2.

Almost every country in the world has now gone through 2 or 3 waves of the COVID-19 pandemic and, in most of them, incidence remains high although it has recently been falling almost everywhere. everywhere. Although the vaccine is being rolled out in many places, it is at a very slow pace with most countries facing shortage and distribution problems. This means another flare-up is likely in many places even if the worst of the pandemic is probably behind us. While lockdowns and other stringent restrictions had high levels of support when the first wave hit, this is no longer true and, as we are entering the last phase of the pandemic, the debate about how to deal with it has never been so intense. Sweden went a different route last spring by foregoing a lockdown and, while it remains widely vilified for this decision, even some people who thought it was a mistake at the time have changed their mind and now think other countries should follow Sweden’s example and seek to contain the epidemic without stringent restrictions such as stay-at-home orders, outright business closures, etc.

I’m one of them. Back in spring, I was in favor of lockdowns, but since then I have reached the conclusion that lockdowns and other stringent restrictions do not make sense from a cost-benefit perspective. I now think that, even with the information we had at the time, supporting lockdowns was the wrong call because even though I insisted that it was only a temporary solution and that we should be ready to revise our view as more evidence came in, I should have known that people would not and that lockdowns would quickly become institutionalized. However, in this post, I will not be arguing for this view. I only want to argue that, regardless of what should have been done last spring, the data we have accumulated since then show very clearly that, whatever the precise effect of lockdowns and other stringent restrictions, it is not nearly as large as we might have thought, so their costs far outweigh their benefits and we therefore should avoid them where they are not currently in place and start lifting them immediately where they are.

Back in March, there was at least a case in favor of lockdowns. Indeed, we didn’t know at the time how difficult it would be to reduce transmission, but we knew that R_0 had been measured at ~2.5 and that in most countries thousands of people were already infected, which meant that unless transmission was reduced quickly more than 90% of the population might be infected in a few weeks. Since the evidence suggested that the infection fatality rate (IFR) was around 1% even when people received proper treatment, this in turn meant that in a country like the United States, between 2 and 3 million people would die even if hospitals were not overwhelmed. However, if the virus swept through the majority of the population in a few weeks, the hospitals undoubtedly would be, so most people would not receive proper care, the IFR would consequently rise way above 1% and the number of deaths would actually be much higher. A lockdown would cut transmission and, while it could not prevent a large part of the population from getting infected eventually, because we couldn’t stay locked down forever, it would “flatten the curve” and prevent hospitals from being overwhelmed and the rise of the IFR this would cause.

But while this line of thought was reasonable at the time, it has become clear that it rested on a flawed premise. Even without a lockdown and stringent restrictions, incidence always starts falling long before the herd immunity threshold is reached. In fact, not only are lockdowns and other stringent restrictions unnecessary to prevent the virus from ripping through most of the population in a few weeks, but they don’t seem to be making a huge difference on transmission. This makes a more liberal approach, not unlike what Sweden has done, far more appealing from a cost-benefit perspective and should have radically altered the policy debate. Unfortunately, this has largely not happened, because most people still believe the flawed assumptions of the original argument for lockdowns and have kept moving the goalposts. At any rate, this is the case I will make in this post.

The alternative to lockdowns and other stringent restrictions is not herd immunity

The first thing everyone should acknowledge at this point, although many people still don’t, is that whatever the precise effect of lockdowns and other stringent restrictions is, it can’t be huge. In particular, it’s certainly not the case that, in the absence of a lockdown, the virus quickly sweeps through the population until the epidemic reaches saturation. There is no need for anything fancy to convince yourself of that, you just have to eyeball a few graphs. Here is my favorite:

As you can see, Sweden was ahead of the rest of the EU after the first wave, but the rest of the EU has caught up since then and now the number of COVID-19 deaths per capita in Sweden is about average.

Of course, policy is not the only factor affecting the epidemic (that’s the point), so this graph does not show that lockdowns and other stringent restrictions have no effect, but if policy mattered as much as pro-lockdown advocates claim, it would look completely different. Indeed, although Sweden has tightened restrictions to fight the epidemic in recent months and the other EU countries have on the contrary used less stringent restrictions during the second/third wave, restrictions in Sweden remain much less stringent than almost everywhere else in Europe and this was already true during the first wave. In particular, even if they have to close earlier and respect stricter health regulations, bars and restaurants are still open and there is no curfew. If lockdowns and other stringent restrictions were really the only way to prevent the virus from quickly sweeping through the population until saturation is reached, the number of deaths per capita in Sweden would be 3 to 15 times higher and that graph would look very different. Yet people continue to talk as if lockdowns were the only way to prevent that from happening. In fact, as we shall see, most scientific papers about the effect of non-pharmaceutical interventions implicitly rest on that assumption. It’s as if reality didn’t matter, but it does, or at least it should.

The average number of COVID-19 deaths per capita for the EU without Sweden hides a significant amount of heterogeneity:

However, as you can see, the picture remains very similar even when you disaggregate and still shows a lot of convergence.

Moreover, although there remain significant disparities between EU countries, what is striking, if you have kept yourself informed about the various policies used to contain the epidemic in various EU countries, is the lack of any clear relationship between policy and outcomes:

For instance, Finland is the country with the smallest number of COVID-19 deaths per capita, yet although it locked down last spring, restrictions in Finland have been even more relaxed than in the much-reviled Sweden for months. Of course, I’m not saying that you couldn’t find some kind of relationship if you looked close enough and used enough fancy statistics, but the point is precisely that you’d have to look very close.

The situation is very similar in the US. You may recall that, back in April, The Atlantic published a piece called “Georgia’s Experiment in Human Sacrifice“ decrying the decision by the governor of that state to lift many restrictions. So let’s have a look at the result of this so-called experiment:

As you can see, the number of COVID-19 deaths per capita did increase and eventually caught up with the average of the US (although this graph doesn’t show any clear effect of Governor Kemp’s decision to lift many restrictions at the end of April), but the carnage predicted by opponents of that decision never happened and the number of COVID-19 deaths per capita in Georgia is actually slightly under the US average. Again, Georgia may have characteristics that protected it from a worse outcome and this graph obviously doesn’t show that the death toll would not have been lower with more stringent restrictions, but it still makes clear that policy isn’t as powerful a factor as Kemp’s critics assumed and as many people still assume.

As in the case of the EU, if you disaggregate, the graph reveals a lot of heterogeneity between states, but the same pattern of convergence is also present:

Some of the states that were relatively spared during the first wave remain less affected than average, but the difference has shrunk and, in many other cases, they have caught up with the US average and sometimes even exceed it.

Again, although there remain significant disparities between states, the role of policy doesn’t jump out at you if you know what different states have done to deal with the pandemic:

Again, I’m not saying that you couldn’t find a relationship with policy if you looked hard enough, but it would take some work and no amount of statistics should convince anyone who has seen those graphs that lockdowns and other stringent restrictions are the only way to prevent the virus from quickly sweeping through the population until saturation is reached.

Even if someone has been able to find a large effect of non-pharmaceutical interventions on transmission with a more sophisticated statistical analysis, the fact it doesn’t jump at you when you look at this kind of simple graphs should make you skeptical of that finding and, the larger the effect, the more skeptical you should be, because if non-pharmaceutical interventions really had a very large effect it should be easy to see it without fancy statistics. I think that, in general, one should be very suspicious of any claim based on sophisticated statistical analysis that can’t already be made plausible just by visualizing the data in a straightforward way. (To be clear, this doesn’t mean that you should be very confident the effect is real if you can, which in many cases you shouldn’t.) That’s because sophisticated statistical techniques always rest on pretty strong assumptions that were not derived from the data and you should usually be more confident in what you can see in the data without any complicated statistical analysis than in the truth of those assumptions. So visualizing the data provides a good reality check against fancy statistical analysis. By following this principle, you will sometimes reject true results, but in my opinion you will far more often avoid accepting false ones. As we shall see later, not only is the literature on the effect of non-pharmaceutical interventions no exception, but it’s actually a great illustration of the wisdom of that principle.

Another way to convince yourself that, whatever the precise effect of lockdowns and other stringent restrictions, it’s almost certainly not huge is to compare the timing of non-pharmaceutical interventions with the evolution of the epidemic. Indeed, while you can find plenty of examples that are compatible with the pro-lockdown narrative, as long as you don’t cherry-pick the data, you can also find plenty of examples that are difficult to reconcile with that narrative. In particular, if you look at the data without preconceived notions instead of picking the examples that suit you and ignoring all the others, you will notice 3 things:

1. In places that locked down, incidence often began to fall before the lockdown was in place or immediately after, which given the reporting delay and the incubation period means that the lockdown can’t be responsible for the fall of incidence or at least that incidence would have fallen even in the absence of a lockdown.

2. Conversely, it’s often the case that it takes several days or even weeks after the start of a lockdown for incidence to start falling, which means that locking down was not sufficient to push R below 1 and that other factors had to do the job.

3. Finally, there are plenty of places that did not lock down, but where the epidemic nevertheless receded long before the herd immunity threshold was reached even though incidence was increasing quasi-exponentially, meaning that even in the absence of a lockdown other factors can and often do cause incidence to fall long before saturation.

I’m just going to give a few examples for each category, but I could talk about many others in each case and, if you spend a bit of time looking at the data, you will have no problem finding more yourself.

A good example of a place where incidence started falling before the lockdown was in place is France during the second wave:

We can see clearly that had already stopped increasing by the time the lockdown came into effect.

Since the incubation period lasts almost a week on average and people generally don’t get tested immediately after the onset of symptoms, there is absolutely no way the fall of incidence was due to the lockdown, although we can’t exclude that it accelerated the fall once it came into effect. Indeed, when you infer the number of infections from the data on death by using the infection-to-death distribution to reconstruct when people were infected based on when they died, you find that the peak was reached about a week before the lockdown started, even without taking into account the reporting delay in the data on deaths. This method is not very precise and the specific date of the peak shouldn’t be taken seriously, but it’s clear that incidence started falling before the lockdown. This is so obvious that it’s clear even in all-cause mortality data, which have the inconvenience of not including only deaths due to COVID-19, but the benefit of being higher-quality since deaths are recorded by date of death and not by date of report.

Yet another way to see that is to disaggregate the data geographically and look at different areas separately. For instance, if you look at the number of cases in Paris, you can clearly see that incidence started falling before the lockdown:

As you can see, by the time the lockdown came into effect, incidence had already been falling for a few days. You could argue that it’s because of the curfew, though it’s unclear the timing is consistent with that hypothesis either and there are regions where incidence started falling before the lockdown despite the absence of curfew, but in any case it’s definitely not because of the lockdown.

Unfortunately, being as clueless as ever, the epidemiologists who advise the French government still don’t seem to have gotten the memo even 4 months later. Indeed, in a paper they recently published about machine learning models they created to predict the short-term evolution of the epidemic, they note that all of them “over-estimate the peak since the lockdown”, but claim it’s because the date of the lockdown “could not have been anticipated”, which is obviously not the explanation since again the peak of infections was reached before the lockdown. If you take another look at the graph for the country as a whole, it’s also interesting to note that incidence started to rise again about 2 weeks before the lockdown was lifted on December 15. You can say that it’s because people started to relax and this reduced compliance, but you don’t actually know that and, even if that were true, it’s the effectiveness of the actual lockdown that we’re interested in, not a theoretical lockdown where compliance remains the same throughout. Indeed, you can’t ignore the problem of non-compliance, which becomes even more important as time goes by and “lockdown fatigue” sets in.

The UK during the second wave also provides a very interesting example, even though it’s not clear that incidence started falling before the second national lockdown started on November 5. Indeed, the Office for National Statistics has been conducting the COVID-19 Infection Survey, a repeated cross-sectional survey of SARS-CoV-2 swab-positivity in random samples of the population since last May, so we have much better data to follow changes in incidence than in other countries, where we have to rely on data on non-random tests that are extremely noisy and subject to various biases. Here is a chart from the December 11, 2020 report, which shows the proportion of people in England that tested positive in that survey:

If you look at the point estimates, the peak was reached during the week between November 8 and November 14, but the confidence intervals of the estimate overlap for any week between October 17 and November 21, so we can’t rule out the hypothesis that it was reached before the lockdown started. But regardless of when exactly the peak was reached, what is certain from this graph is that the growth rate of positivity started to collapse long before the lockdown started, so there is every reason to believe that incidence would have fallen even without a lockdown.

If you look at the results disaggregated by region in the same report, it does look as though positivity started to fall before the lockdown in some regions:

However, since a three-tiered framework of restrictions had been introduced in October, it could be argued that the decline in positivity was due to the restrictions that were implemented in those regions before the lockdown came into effect. (The same thing could be said about France during the second wave, where a curfew was put in place in some regions before a national lockdown was implemented.) What is more interesting is that, in several regions, the lockdown is not clearly associated with any change in positivity, which is hard to reconcile with the hypothesis that lockdowns and stringent restrictions have a very large effect. Although those results involve a lot of modeling and shouldn’t be taken at face value, this is another thing that we see again and again in the data of several countries when they are disaggregated by region, which has been largely ignored even though, or perhaps because, it’s at odds with the pro-lockdown narrative.

Next, let’s move to the second type of phenomenon I identified above, namely places where a lockdown was implemented but wasn’t associated with any fall of incidence. The most striking example of that phenomenon is arguably Peru, which had the worst epidemic in the world despite locking down very early:

Pro-lockdown advocates like to insist that lockdowns are most effective when they are done early and the rules are stringent. Peru went on lockdown merely 9 days after the first case and before anyone had even died of COVID-19. Moreover, with the exception of China, the rules were stricter than anywhere else in the world and the government tightened them several times during the first 2 weeks of the lockdown. At one point, only men were allowed to leave their home on certain days and only women the rest of the week, while nobody was allowed to do so on Sunday. Grocery stores had to close at 3pm and the military was patrolling the streets to enforce the curfew. If there is one country where a lockdown should have prevented the epidemic from getting out of control, it was Peru, but it instead had the world’s highest known excess mortality rate in 2020.

There are other examples of lockdowns that didn’t show any clear effect. Ironically, one of them is the lockdown in Melbourne that started in July and is often cited as an example by proponents of the so-called “zero covid” strategy, but I will discuss that later. Rather than look at clear-cut examples, I would like to discuss the third national lockdown in the UK, which is a very interesting case because, depending on what data you look at, you can argue that incidence started to fall immediately after it came into effect, that it started to fall before that or that it didn’t start to fall until much later. Thus, it illustrates the danger of inferring that a lockdown “worked” by visually inspecting a chart that shows the daily number of cases and noticing that it started falling shortly after the lockdown came into effect, as pro-lockdown advocates constantly do. Indeed, if you look at a graph showing the daily number of cases in England during the third wave, it certainly looks as though the lockdown worked exactly as expected:

As you can see, the daily number of cases peaked a few days after the lockdown came into effect, which given the average incubation period seems roughly consistent with the hypothesis that transmission was suddenly cut by the lockdown.

This is the graph most pro-lockdown advocates are looking at and the inference they make, but it doesn’t account for the reporting delay, which pushes back further the time when incidence started falling. Fortunately, the Office for National Statistics also publish data on the number of cases by date of specimen, so we can plot the daily number of cases without the reporting delay:

As you can see, this tells a different story, since it shows that the number of cases actually started falling a few days before the lockdown came into effect. Since the incubation period lasts almost a week on average and people generally don’t get tested immediately after symptoms onset, this suggests that the number of infections started to fall at least a week before the lockdown came into effect, which would make England during the third wave another example of the first type of phenomenon I identified above.

Remarkably, when you disaggregate and look at the same data by region, every region exhibits a very similar pattern:

This is remarkable because, on December 19, new restrictions were applied to London and parts of the East and South East that in some ways prefigured the lockdown, so if stringent restrictions had a large effect you would expect to see more pronounced differences between regions. It does look as though infections started to fall a little bit sooner and then fell a little bit faster in the regions where more stringent restrictions were in place, but the effect is hardly impressive and, as I will explain later, the results doesn’t mean that it was causal and there are good reasons to doubt that it was.

But things are even more complicated with the third national lockdown in the UK. Indeed, while it looks as though incidence started to fall before the lockdown came into effect when you look at the data on cases, the REACT-1 study, another repeated cross-sectional survey of SARS-CoV-2 swab-positivity in random samples of the population of England whose 8th round was conducted in the 2 weeks following the beginning of the lockdown, didn’t find any fall in the positivity rate immediately after the lockdown started:

As you can see, the positivity rate didn’t start falling until January 16, more than 10 days after the lockdown came into effect. Even taking into account the time it takes between the moment someone is infected and the moment the virus has replicated enough for a PCR test to come back positive, this seems too late for the lockdown to explain it. The authors of the report suggests that it may be due to a temporary increase in household transmission driven by the start of lockdown, as people started to spend more time with their family, but this is merely a conjecture and, as the report also notes, data on mobility don’t show any effect of the lockdown.

The results disaggregated by region are once again show a diversity of patterns that is hard to reconcile with the hypothesis that restrictions have a huge effect on transmission:

As you can see, in most regions the positivity rate doesn’t seem to have decreased much or at all even 2 weeks after the beginning of the lockdown, except in South West where robustly decreasing prevalence can be observed and East Midlands where prevalence actually seems to have increased during that period. I don’t see how anyone can look at those data and conclude that the lockdown was the main factor driving the epidemic in England during that period, which is probably why pro-lockdown advocates generally ignore them.

The COVID-19 Infection Survey also found a great deal of heterogeneity in the trajectory of the positivity rate in different regions, which is not what you’d expect if the lockdown had a massive effect on transmission:

It’s also remarkable that, in several regions, the results are strikingly different from what the REACT-1 study shows. Of course, the results are not straightforwardly comparable, if only because the COVID-19 Infection Survey uses a different modeling approach. But the fact that you can get such different results is still pretty telling, because if the lockdown really had the kind of massive effect that pro-lockdown advocates claim, not only would you see a more homogenous response across regions, but differences in modeling choices presumably wouldn’t result in such inconsistent results.

But what’s even more striking is that data from repeated cross-sectional surveys of SARS-CoV-2 swab-positivity in random samples of the population tell a completely different story from data on cases, which as we have seen suggest that incidence started falling everywhere about a week before the lockdown started. There are many possible explanations for this apparent inconsistency. For instance, it could be that infections started to fall earlier among older people, who are more likely to be symptomatic and get tested, but continued to increase among younger people for some time. However, this is not what the data from the COVID-19 Infection Survey show, so it probably isn’t the explanation. Another possible explanation is that data from the REACT-1 study and the COVID-19 Infection Survey, even though they rely on random samples of the population, are not very good. Indeed, the response rate seems pretty low in both cases, so inferring the prevalence of infection in the population from the sample may be misleading. Moreover, testing by PCR can detect viral RNA in swabs for a while after the infection was successfully fought off by the immune system, which probably makes it difficult to pick up small, gradual changes in prevalence even in a large sample. Of course, the problem could still come from the data on cases, it’s possible that something other than age changed among the people who were infected that resulted in a fall of the number of cases even though the number of infections was still increasing or staying roughly constant.

I spent some time on the case of the third national lockdown in England because it illustrates that, even when it looks as though a lockdown is clearly working, things get a lot muddier when you take a closer look at the data. The case of England is particularly interesting because, unlike in many places where only the data on the number of cases by date of report are available, we have lot of different sources of data on the epidemic in England, but I’m sure we’d reach a similar conclusion elsewhere if we had more data. The truth is that, based on the data we have, it’s impossible to tell whether the number of infections started to fall before, shortly after or as late as 10 days after the lockdown came into effect. Note that I’m just talking about what we can tell about the timing of the epidemic relative to that of the lockdown here, but as I will explain later, we couldn’t infer that the lockdown was responsible even if we knew for sure that incidence started to fall shortly after it came into effect, so the pro-lockdown case is even weaker than it looks. In general, I hope this discussion has illustrated how incredibly noisy the data about the pandemic are, even in the UK which has much better data than virtually any other country. This is important because all the studies that people tout as proof that lockdowns and other stringent restrictions have a huge effect on transmission are based on such very low-quality data, but I will go back to the scientific literature on the effect of non-pharmaceutical interventions later.

For the moment, I would like to turn to the third type of phenomenon I identified above, namely places that didn’t lock down but where incidence nevertheless started falling after a period of quasi-exponential growth. Examples of this type are for me the most important because they show that, even without a lockdown and with far less stringent restrictions than those currently in place in France and many other countries, a phase of quasi-exponential growth of incidence never lasts very long and the epidemic always ends up receding long before the herd immunity threshold is reached. The best known example is of course Sweden, which has never locked down and where restrictions are much less stringent than almost anywhere else in Europe, but where incidence didn’t continue to increase exponentially until the herd immunity threshold was reached but actually started to fall way before that, be it during the first wave last spring or during the second wave this winter:

The data on cases are misleading for the first wave, because Sweden was testing very little at the time, so it looks as though incidence remained low, but the data on ICU admissions show very clearly that’s not what happened. What is also clear is that, despite the lack of lockdown or very stringent restrictions, the epidemic quickly reached its peak and began to decline by the beginning of April. For the second wave, Christmas and New Year’s Day clearly affected the data on cases, but we can still see that incidence declined for several weeks starting from the end of 2020 (even though it recently started to increase again), a conclusion that is further strengthened by the data on ICU admissions. As during the first wave, the epidemic eventually receded without a lockdown or a curfew and while small businesses, bars and restaurants remained open, even though the sale of alcohol is prohibited from 8pm onwards and a number of restrictions are still in place.

Many people think that Sweden is unique, but that’s not the case at all, there are many other places beside Sweden that have not locked down and where the epidemic still ended up receding long before saturation. For example, it’s what happened in Serbia this fall, where there was no curfew and bars and restaurants remained open during the week even at the height of the second wave, even though they had to close earlier than usual on weekdays and completely on weekends:

Again, it’s not as if there were no restrictions in Serbia, but they are much less stringent than in France and most other European countries. However, this didn’t prevent the epidemic from receding, even though it is clear that the country is very far from having reached the herd immunity threshold. Recently, incidence started increasing again, but it does not change what happened before and this is perfectly consistent with the explanation I will propose in the next section.

In the US, many states also refused to lock down after the first wave, but that didn’t stop the epidemic from eventually receding everywhere. For instance, this is what happened in Florida, one of the most populous states in the US, both last summer and this winter:

I also show the daily number of deaths because, like everywhere else, Florida tested very little during the first wave and the data on cases are therefore misleading.

Florida did lock down in April, but since then Ron DeSantis, the state’s governor, has refused to do it again. Even at the height of the second wave, bars and restaurants remained open and there was no curfew except in Miami-Dade County, although the sale of alcohol was banned in bars at the end of June. In September, the governor ordered that all health restrictions be lifted in bars and restaurants, prohibiting even counties and cities from imposing such restrictions locally, which did not result in a resurgence of cases. When incidence began to rise again in November, despite the fact that experts and the media demanded that he impose stringent restrictions again, he refused to give in and the state remained completely open. Nevertheless, as you can see on the graph, the third wave also started to recede at the beginning of the year and incidence in Florida has been steadily falling since then. While there have been almost no restrictions since September, which actually makes Florida a far more extreme counter-example to the pro-lockdown narrative than Sweden, the cumulative number of deaths per capita in that state is barely higher than in France, where there is a curfew of 6pm, bars and restaurants have been closed everywhere since the end of October, etc. One could make a similar comparison with other European countries where restrictions have been very stringent or, as we shall see, with California, where restrictions are also far more stringent and where there even was a lockdown.

I could go on like that for hours, because there are plenty of examples that contradict the claim that, without a lockdown, incidence continues to rise quasi-exponentially until the herd immunity threshold is reached. Not only is this patently false, but in developed countries at least (I will go back to this point below), the epidemic ended up receding long before that point in every place that did not lock down, without a single exception. Unfortunately, most people don’t know that, because there is a huge bias in the way the media and people on social networks talk about the pandemic. For example, as long as the incidence was rising very rapidly in Sweden, I would see graphs every day showing the explosion of cases accompanied by alarmist and/or sarcastic commentary about the Swedish strategy, but curiously since incidence started falling I don’t hear about Sweden anymore. It’s the same thing with Florida, North Dakota, South Dakota, Georgia and every other place that did not lock down and where almost everything remained open even at the height of the second and/or third waves. Similarly, almost nobody has ever heard about what happened in Serbia, which adopted a strategy very similar to that of Sweden during the second wave.

Conversely, when a lockdown or stringent restrictions fail to quickly produce visible results, as in California last December, you don’t hear from that place again until incidence finally starts falling, which again it always does eventually with or without a lockdown or stringent restrictions. At which point, you start hearing about that place again, which becomes the latest proof that lockdowns are effective even though it’s hardly obvious upon taking a close look at the data, as we have seen in the case of the third national lockdown in England. When a lockdown has failed to produce any visible results even after 2 weeks, but the media can’t ignore it for one reason or another, we are assured that it’s because it wasn’t strict enough. Of course, pro-lockdown advocates never say in advance what restrictions will be stringent enough, nor after how long we may conclude that they didn’t work, so they can never lose.

When incidence starts rising again in places that have not locked down, which will probably happen in at least some of them, the same people who had forgotten their existence will start talking about the “Swedish disaster“ or the “Georgia’s experiment in human sacrifice“ again. Cases that support the view that only very stringent restrictions can prevent a disaster are talked about constantly, while any counter-example to that view is systematically ignored. For the most part, people are not even being intellectually dishonest, it’s just confirmation bias on steroids. This is made worse by the fact that the issue has been politicized, though not always along traditional political divides, so people have to toe the party line. I know many people who understand what I’m saying perfectly well, but they will never say it publicly or say it in a much watered down form, because they’re afraid of what people on their team would think. The issue of lockdowns has practically become a religion for some people and they do not easily forgive slights to their god.

When you point out counter-examples to their view, pro-lockdown individuals always have a way to explain them away. They are always ready to bring up a difference, real or imagined, between places that have not locked down and others that did not which they believe explains why the epidemic wasn’t significantly worse in the former than in the latter. In the case of Sweden, what always comes up is population density. If Sweden did not have more COVID-19 deaths than many countries that have put in place far more stringent restrictions, so the argument goes, it’s because it has a very low population density. The problem is that, when you look at the data, there is no clear relationship between population density and the number of COVID-19 deaths per capita:

I have restricted myself to Europe, which is relatively homogeneous in demographic and economic terms, to reduce the risk that even a strong association between population density and the number of COVID-19 deaths per capita be hidden by other, even more important factors, such as the proportion of the population over 60. (I would like to thank Antoine Lévy for providing me with this dataset, which he constructed for the purposes of his analysis in a recent paper, but it goes without saying that none of the opinions I express in this post should be attributed to him.) I also used population-weighted population density rather than population density, because population density is often extremely misleading because even in a very large country, people are usually concentrated in a tiny part of the territory.

As you can see on this graph, even when you restrict yourself to a group of countries that are relatively homogenous in economic, cultural and demographic terms, there is no clear relationship between population density and the number of COVID-19 deaths per capita. You can also see that Serbia, where as I have already noted the second wave has receded without a lockdown, has a population-weighted population density roughly equal to that of France and other countries where pro-lockdown advocates assure us Sweden’s strategy could never work because population density is higher. The same thing could be said about many other places, such as Florida, where the same thing happened. Of course, it doesn’t mean that, other things being equal, population density doesn’t result in higher transmission and in fact I have no doubt that it does, but clearly the effect is not as large as one might have thought, otherwise it would be easier to detect. This example illustrates a recurring phenomenon in debates about the pandemic. People make wild conjectures that often aren’t even supported by the data we have, but assert them as if they were established fact. We’ll see another example of this phenomenon when I briefly discuss what happened in Asian countries that managed to keep the epidemic under control without lockdowns.

Another argument that is often made is that you shouldn’t compare Sweden to countries like France, the UK or Belgium but only to its neighbors, because due to cultural proximity or whatever they provide a better counterfactual of what would have happened in Sweden if the government had decided to lock down. However, as I explained elsewhere, not only is this claim largely gratuitous, but it’s demonstrably false. Indeed, when you infer the number of infections during the first wave from the number of deaths, you find that, by the time its neighbors decided to lock down, the epidemic was already far more advanced in Sweden. Thus, even if Sweden had locked down around the same time as its neighbors and we assume that it would have suddenly cut transmission by a very large factor, which as we have seen is almost certainly false, there would still have been far more COVID-19 deaths in Sweden because a lot more people had already been infected and it would have taken longer for incidence to go down since it was starting from a much higher level. Frankly, it’s incredible that so many people still believe that policy explains most of the difference in outcomes between Sweden and its neighbors. Even if I were wrong about what happened during the first wave, as I already noted, Finland remains almost entirely spared by the pandemic even though restrictions have been even less stringent than in Sweden for months. The same thing could be said about most of Norway. Although nobody knows what they are, there are clearly factors beyond policy that play a major role and explain why Sweden’s neighbors have largely been spared by the pandemic, but people continue to make this comparison as if it proved that Sweden’s failure to lock down explains most of the difference.

Pro-lockdown advocates like to bring up culture to explain away inconvenient facts, but while I have no doubt that culture affects the course of the epidemic, cultural explanations have repeatedly proved wrong since the beginning of the pandemic, without reducing people’s appetite for them. For instance, when it became clear that the holocaust that pro-lockdown advocates predicted in Sweden had failed to materialize and that COVID-19 mortality was not particularly high over there, many of them started to say that Sweden’s strategy could not be replicated in other countries not just because of population density but also because they lacked the Swedish culture of compliance with government rules. Thus, when incidence started to explode in Spain a few weeks ago and the government refused to lock down (it even prevented local governments from locking down when they tried), they naturally denounced that decision as irresponsible, since what Sweden did could never be replicated in a Latin country such as Spain. Instead, I predicted that incidence would soon begin to fall, which is exactly what happened:

In fact, although I couldn’t have known it when I made that prediction, the number of cases had already started to fall. That’s because data on cases by date of symptoms onset take a while to be compiled, so we only had data on cases by date of report and there is a significant reporting delay.

Now that incidence has collapsed, some of the people who predicted the apocalypse have done a U-turn and now claim there was a de facto lockdown in Spain, on the ground that many regions had put in place stringent restrictions even though they were prevented by the national government from implementing a complete lockdown. But it’s still the case that almost everywhere in Spain restrictions were less stringent than in the UK or even France, which is not even locked down but where there is a curfew at 6pm and bars and restaurant are closed except for take-out. Moreover, in some regions (such as Madrid), restrictions remained very limited. Bars and restaurants were allowed to remain open at all time until January 18, 2021 when they were forced to close at 10pm, while a curfew starting at 11pm came into effect. On January 25, the closing time for bars and restaurants was changed to 9pm, while the curfew was advanced to 10pm. In other regions, restrictions were more stringent, sometimes a lot more, but again they remained less stringent than in France or the UK almost everywhere. Thus, I don’t see how anyone can seriously claim that Spain was de facto on lockdown when incidence started to fall, if by that we mean something like what the country did last Spring or what the UK or even France are currently doing. If pro-lockdown advocates in France or the UK really think that, then they should ask that bars and restaurants be reopened over there, but somehow I don’t think that’s going to happen.

Despite the fact that restrictions in Spain ranged from very limited as in Madrid to very stringent as in Murcia, incidence started to fall everywhere around the same time in January:

You may be able to argue that it started to fall a bit earlier and that it has been falling a bit faster in regions with the most stringent restrictions in place, which doesn’t mean that it was because of that, but it still fell everywhere including in regions where restrictions were very limited. In fact, if you look at the timing of the fall and compare it to that of the restrictions in each region, you will generally find that incidence started to fall before the most stringent restrictions came into effect, especially when you take into account the period of incubation. So the prediction that Sweden’s strategy wouldn’t work in Spain because it doesn’t have the right culture proved spectacularly wrong.

I’m sure there are plenty of differences between the places that have locked down and those that have not, and even that some of them affect the epidemic, although the truth is that nobody knows what they are or how exactly they do so. But places that have not locked down or put in place very stringent restrictions are so diverse economically, culturally, demographically, etc. that if incidence nevertheless started to fall long before the herd immunity threshold was reached in all of them, it’s extremely unlikely that it’s because they all happen to have characteristics that make not locking down a viable option, whereas everywhere else this policy would lead to the disaster predicted by pro-lockdown advocates as incidence would continue to increase quasi-exponentially until the herd immunity threshold is reached. At this point we have so many examples, and no counter-examples, that such a claim is akin to magical thinking. It’s far more likely that, whenever and wherever incidence starts increasing quasi-exponentially somewhere, the same mechanisms push below 1 long before the herd immunity threshold is reached even when there is no lockdown or stringent restrictions. In the next section, I propose a theory of what this mechanism could be, which also explains why it often looks as though lockdowns and other stringent restrictions are very effective and why many governments have used them despite their cost and limited effectiveness.

A theory of why lockdowns and other stringent restrictions don’t make a huge difference

Many people assume that, without a lockdown, when incidence starts increasing quasi-exponentially, it will continue to rise in that way until the herd immunity threshold is reached. But as we have seen, this is not what happens and therefore it doesn’t make sense to extrapolate from current growth by assuming it will continue until something like 66% of the population has been infected. It’s true that, in a standard compartmental model, incidence rises quasi-exponentially until the attack rate approaches the herd immunity threshold, but that’s only the case when, among other things, the contact rate is assumed to be constant. However, with or without lockdown, the contact rate never remains constant because people respond to epidemic conditions by changing their behavior, which affects the contact rate and therefore also R. (I will pass over the fact that, beyond the assumption that both the contact rate and the generation interval remain constant, which can easily be relaxed, the model from which the formula that everyone is using to compute the herd immunity threshold is totally unrealistic, in particular because it assumes a perfectly homogenous population, so that we don’t actually know what the herd immunity threshold really is.) Beside, even if this were not the case, given that R has been hovering between 1 and 1.5 for months almost everywhere, we’d still expect the epidemic to start receding long before 66% of the population has been reached anyway.

To the extent that restrictions have any effect on transmission, they presumably have both direct and indirect effects. Direct effects consist in physically preventing certain events that contribute to the spread of the virus. For example, if the government bans large gatherings and the ban is respected, it becomes physically impossible for a single person to infect hundreds of people at the same time. But presumably restrictions also have indirect effects because they send a signal to the population, which can translate into behavioral changes that in turn can affect the contact rate and/or the generation interval. (The contact rate is a quantity used to model how often people meet each other in a way that results in someone getting infected, while the generation interval is the time between the moment someone is infected and the moment they infect someone else.) My theory about the epidemic is that, once you have some basic restrictions in place, such as a ban on large gatherings, then unless perhaps you go very far as the Chinese authorities did in Wuhan (which I think is neither possible nor desirable in a democracy), more stringent restrictions have a rapidly decreasing marginal return because they are a very blunt instrument that has a hard time targeting the behaviors that contribute the most to transmission and people reduce those behaviors on their own in response to changes in epidemic conditions such as rising hospitalizations and deaths. However, as I explain below, it doesn’t mean that their marginal cost also decreases rapidly. For instance, a 6pm curfew as in France probably doesn’t have much impact if any on transmission, but it arguably has a large effect on people’s well-being.

In simple terms, what this means is that, once the authorities have put in place relatively limited restrictions, everything they do after that has an increasingly small effect on transmission and consequently the most stringent restrictions only have a relatively negligible impact on the dynamics of the epidemic. (Again, it’s plausible that it ceases to be true if you go very far as the Chinese authorities did in Wuhan, but even in China we don’t really know for sure that lockdowns were essential to the country’s ability to suppress the virus. Indeed, neighboring countries were able to do the same thing without lockdowns, so I don’t see why people are so confident that lockdowns are what did the work in China as opposed to whatever did the work in other East Asian countries.) If this were not the case, given how much variation in policy there is between regions, the graphs of the cumulative number of COVID-19 deaths in US states or European countries I have shown above would almost certainly look very different. On the other hand, there is very little variation in more limited non-pharmaceutical interventions such as bans on large gatherings, which are in place almost everywhere, so this doesn’t tell us they only have a small effect and I think we have good reasons to think they have a significant one even though ultimately even that is not clear. Again, I’m not claiming that lockdowns and other stringent restrictions have no effect on transmission, I’m just saying that when you look at the data it’s hard to convince yourself they have more than a relatively small effect and it’s impossible to maintain that it’s as large as pro-lockdown advocates claim.

Moreover, when I say that people’s voluntary behavior changes in response to changes in epidemic conditions, I’m not saying that the mechanism is necessarily just the aggregate reduction in social activity. For instance, since presumably not everybody respond in the same way to changes in epidemic conditions, it’s possible that a rise in incidence, which eventually results in a rise of hospitalizations and deaths that scare people into modifying their behavior, temporarily creates more heterogeneity in the population because some people will react more strongly to this change in epidemic conditions than others, which in turn lowers the herd immunity threshold until incidence goes down and eventually people go back to their previous behavior. One could also imagine that behavior changes increase the generation interval, which even keeping R constant would lower the growth rate of the epidemic. Moreover, it’s likely that the type of social activity people engage in and not just how much of it they engage in matters a lot. If people disproportionately reduce the types of social activity that contribute the most to transmission, a relatively small reduction in aggregate social activity could result in a significant reduction in transmission.

In short, I make no hypothesis on the specific mechanisms underlying the feedback mechanism my theory posits at the micro-level, because I don’t think we really understand what’s going on at that level. I just claim that people’s behavior changes in response to changes in epidemic conditions and that whatever the specific mechanisms at the micro-level those behavior changes eventually make the epidemic recede even when a relatively small share of the population has been infected. Of course, I’m not claiming that the feedback mechanism posited by my theory is the only factor driving the dynamics of the epidemics, but I think it’s probably the main factor explaining why over and over again R dropped below 1 in places where the prevalence of immunity just wasn’t high enough to explain that, as shown by the fact that eventually the epidemic blew up again. (There are other possible explanations and most of them aren’t even mutually exclusive with my theory, but for various reasons I won’t get into, I don’t think they can really explain the data.) However, at this point, I think the prevalence of immunity is high enough in many places that it can plausibly explain why incidence is falling even in the absence of any behavior changes. But I doubt that incidence wouldn’t start rising again if everyone returned to their pre-pandemic behavior.

My theory predicts that, in places where the IFR and the hospitalization rate are lower because the population is younger, the virus will be able to spread faster and the attack rate (i. e. the proportion of people who have been infected) will be higher. Indeed, if the feedback mechanism I postulate operates through exposure to information about the number of deaths and hospitalizations, people won’t start changing their behavior enough to push R below 1 until the daily numbers of deaths and hospitalizations scare them. In a place where people are very young, incidence will have to rise much higher than in developed countries, where a large share of the population is over 60, before this happens. For example, pro-lockdown advocates often cite the case of Manaus, a Brazilian city where a study concluded that about 75% of the population had already been infected by October, which didn’t prevent another wave at the beginning of the year. First, I think it’s extremely implausible that 75% of the population had really been infected at the time, since the study is based on a non-random sample and that estimate was obtained after significant corrections to account for antibody waning, while seropositivity never exceeded 44% in any sample. (I also think it’s a bad idea to generalize from what seems like a clear outlier, but let’s put that aside.) In any case, it’s clear that the attack rate in Manaus is much higher than anywhere in the US or Europe, but this is not surprising if my theory is true.

Indeed, the population in Brazil is much younger than in the US or Europe, so although the attack rate climbed much faster over there, the numbers of deaths and hospitalizations have not. According to official statistics, as of December 8, 2020, 3,167 deaths had been attributed to COVID-19 for a population of approximately 2.2 million, which corresponds to a rate of about 1,438 deaths per million. By comparison, at this point, 11,593 deaths had been attributed to COVID-19 in Madrid. Since that city has a population of about 3.3 million, this corresponds to a death rate of approximately 3,470 per million. Thus, by December 8, the number of COVID-19 deaths per capita was actually higher in Madrid than in Manaus and presumably the same thing was true of the number of hospitalizations. However, even if you don’t buy that 75% of the population had already been infected by October in Manaus, the attack rate was no doubt much higher than in Madrid where seroprevalence was only ~11% in May and the vast majority of deaths were recorded before that. But if my theory is true, there is nothing surprising about that, since it’s only to be expected that it would take longer for people to change their behavior in a place where it takes longer for hospitalizations and deaths to start piling up because the population is younger. Thus, not only are such cases not counter-examples to my theory, but they’re actually predicted by it. I fully expect that, by the time the pandemic is over, we’ll find that the attack rate is higher in places with a younger population even controlling for various relevant variables.

Of course, as I have formulated it, this theory is very vague. In particular, I don’t give any precise figure to clarify what I mean by “rapidly diminishing marginal return” or “not very large effect”, but the truth is that I don’t think you can say anything more precise and people who claim otherwise are trying to fool you or are fooling themselves. I constantly see people on both sides of the debate throwing studies at each other that purport to estimate the effect of non-pharmaceutical interventions and allegedly prove that lockdowns and other stringent restrictions either work or don’t work. Those studies give very precise estimates of the effect of non-pharmaceutical interventions with confidence intervals that look very “scientific”, but all of that is completely meaningless because the models are poorly specified, the studies are plagued by omitted variable bias, measurement error, simultaneity, etc. Just remember how intractable it was to even figure out exactly when incidence started to fall in England, where there are much better data than virtually anywhere else in the world, then just imagine trying to disentangle causality in that mess with far noisier data. No wonder that you can find such inconsistent results in the literature on the effect of non-pharmaceutical interventions. In my opinion, the only studies that you may be able to take kind of seriously are those that use a quasi-natural experiment to estimate the effect of restrictions in a single country, such as this study on locally imposed lockdown in some Danish municipalities last November, which found no clear effect. But the conclusions of such studies can’t easily be generalized to other countries, so even they are not that useful.

However, I know that studies published in prestigious scientific journals exert a strong pull on people, so let me say more about the literature on the effect of non-pharmaceutical interventions. There are so many studies that claim to show that restrictions have a very strong effect on transmission, and so few people who have actually looked at them in detail, that I know people won’t take seriously my theory unless I do. In fact, when you take a close look at those studies, it becomes clear that none of them can possibly refute my theory and that all of them are completely unreliable if my theory is true. Most studies about the effect of non-pharmaceutical interventions fall roughly into 2 categories. First, you have studies that fit an epidemiological model, typically a compartmental model of some kind, on epidemic data. Non-pharmaceutical interventions are assumed by the model to affect transmission in a certain way and their effect is estimated by fitting the model. The other type of studies use econometric or machine-learning methods to estimate the association between non-pharmaceutical interventions and the growth rate of the epidemic or some related quantity such as R.

The most famous example of the first type of study is probably Flaxman et al.’s paper that was published in Nature last June and has already been cited almost 750 times. This paper concluded that non-pharmaceutical interventions and lockdowns in particular had saved more than 3 million lives in Europe alone during the first wave and is still cited all the time by pro-lockdown advocates. I have already written a very detailed take-down of that study, which I strongly encourage you to read, so I’m not going to go over it again. To show how ridiculous the paper is, it suffices to say that, in order to obtain that estimate, the authors used a counterfactual in which more than 95% of the population had been infected by May 4 in every country they included in the study. Of course, even 9 months later, there is not a single country in the world as far as we know and certainly no country in Europe where the attack rate is even close to that. This is one of several little details the authors of that study decided not to state in the paper. The fact that such a preposterous estimate is still being taken seriously by so many people, including professional epidemiologists, tell you everything you need to know about how broken the scientific literature on the effect of non-pharmaceutical interventions is.

As I explain in my post about this study, their own results actually support my theory that, once a few very limited restrictions are in place, voluntary behavioral changes are enough to push R below 1 long before the herd immunity threshold is reached. Indeed, they found that non-pharmaceutical interventions in Sweden, where there was no lockdown and restrictions were very liberal, had reduced transmission almost as much as in the rest of Europe. Nevertheless, they concluded that only lockdowns had a meaningful effect on transmission, because they included a country-specific effect in the model that allowed the effect of the last intervention to vary in each country. In every country besides Sweden, the last intervention was a lockdown and the country-specific effect is never very large, but in Sweden the last intervention was a ban on public events and the country-specific effect was gigantic. As I noted in my reply to Andrew Gelman’s comment about my post, the result was that while their model found that banning public events only reduced transmission by ~1.6% everywhere else, it found that it had reduced it by ~72.2% in Sweden, almost 45 times more. Of course, this never happened, there is just no way unless you believe Sweden is full of anti-covid magical fairies that banning public events was 45 times more effective in Sweden than anywhere else.

The fundamental problem with this paper is the same as with basically every other paper in that category I distinguished above and it’s that it assumes that only non-pharmaceutical interventions affect transmission. Thus, despite what people like the folks behind The Covid-19 FAQ continue to claim (even though I already explained to them why it was demonstrably false), there is no way studies of that sort could ever show that voluntary behavior changes wouldn’t push R below 1 long before the herd immunity threshold is reached even in the absence of a lockdown, because they literally rely on models that implicit assume that voluntary behavior changes have no effect whatsoever on transmission. This is not just true of Flaxman et al.’s paper, but also of several other highly-cited studies, such as Brauner et al.’s paper in Science or more recently Knock et al.’s paper about the epidemic in England. Basically, what they do is assume that R or a related quantity such as the contact rate is affected by non-pharmaceutical interventions in a certain way, then fit the resulting model to the data to estimate the effect each of those interventions has. At best, what this kind of study can do is answer the question: if we assume that only non-pharmaceutical interventions affect transmission, and make a bunch of other largely arbitrary assumptions, what effect did each non-pharmaceutical intervention had on transmission? But we know that non-pharmaceutical interventions are not the only thing affecting transmission, so papers that follow this approach have no practical relevance whatsoever and predictions based on them are completely meaningless.

A second type of study doesn’t use an epidemiological model but tries to establish correlations between non-pharmaceutical interventions and the growth rate of the epidemic or some related quantity such as with traditional econometric or sometimes machine-learning methods. Basically, what they do is look at the epidemic in a bunch of different countries/regions and try to find if non-pharmaceutical interventions are associated with a reduction in the rate at which it grows, which is the case if the epidemic tends to grow less when non-pharmaceutical interventions are in place. The fundamental problem with this approach is that, if I’m right that people respond to epidemic conditions by modifying their behavior when hospitalizations and deaths start blowing up, then the epidemic’s growth rate will tend to start falling when the authorities decide to implement non-pharmaceutical interventions, because the people in charge also tend to do that when hospitalizations and deaths increase. So this kind of study would probably find a correlation between non-pharmaceutical interventions and a reduction of the epidemic’s growth rate even if the former didn’t have any effect on transmission, because the changes in epidemic conditions that make the authorities inclined to implement non-pharmaceutical interventions also make people change their behavior in ways that reduce transmission.

Similarly, it’s likely that if I gave you a pill that only contains sugar but told you that it’s a medicine that makes fever go down and you were the sort of person that only takes medicine when they’re at the point of death, you’d find that your temperature generally starts going down soon after you take it. But it would be wrong to conclude that it’s because the pill made your temperature go down. Indeed, we know the pill doesn’t do anything, it’s just sugar after all. The reason you’d probably find that your temperature usually goes down soon after you take the pill is that, since you’re the kind of person that only takes pill when they have already been in agony for days, by the time you finally take it, your immune system is mostly done fighting whatever caused the fever in the first place and your temperature was about to start falling anyway. This is what people call endogeneity when they want to sound intelligent, but as you can see, the basic idea is simple enough and anyone can understand it. I think it’s basically what happens with studies that look for correlations between non-pharmaceutical interventions and the epidemic’s growth rate. Again, I’m not saying that non-pharmaceutical interventions have no effect whatsoever, but they typically start around the time people start voluntarily changing their behavior, which hopefully I have convinced you probably has a very large effect on transmission. To be clear, it’s hardly the only problem with those studies, which among other things have to deal with massive measurement error and absolutely terrible data, but that alone makes the whole enterprise hopeless in my opinion.

A good example of this type of study is the paper by Haug et al. that was published in Nature back in November, which is one of the most sophisticated in the second category of studies. The authors used several different statistical approaches to estimate the relationship between non-pharmaceutical interventions and R. Here is the figure that summarizes what they found:

As you can see, if this study is to be believed, while some interventions are not effective, several of them have a large effect on transmission. Many people see that and conclude that it has been scientifically proven that restrictions had a very large effect on transmission, but as I already explained, this kind of study can’t establish causality and we have very good reasons to think their results are extremely misleading. What this means is that, if you use them to predict what is going to happen depending on what policy you implement, you will almost certainly get things catastrophically wrong. But it never occurs to people to check whether studies of that sort perform well out-of-sample, and reviewers apparently don’t ask their authors to do it, so they happily go around making policy recommendations based on papers that have essentially no practical relevance.

In the case of the Haug et al.’s paper, despite the fact that again it’s pretty sophisticated by the standards of that literature, you just have to eyeball a graph of R in various US states during the past few months for 5 seconds to see that it performs horribly out-of-sample:

I didn’t even bother to do this rigorously, but if you look up the restrictions in place in those states during that period and check Haug et al.’s paper, it’s obvious that we should have seen widely different trajectories of R in those states and in particular that it should have been consistently much higher in states like Florida that remained almost completely open than in those like California that have put in place very stringent restrictions, but as you can see that’s not what happened. I only show a handful of states because otherwise the graph would be illegible, but I didn’t cherry-pick and, if you plot R in every state, you’ll see that it follows a very similar trajectory everywhere. You can do the same thing for Europe and you will reach the same conclusion.

Only a handful of studies make a serious attempt to address the endogeneity problem I have identified above. The best is probably the paper by Chernozhukov et al. about what happened in the US during the first wave that was recently published in the Journal of Econometrics, which as far as I know is the most sophisticated attempt to estimate the effects of lockdown policies in the literature. Indeed, unlike most papers in the literature about the effects of non-pharmaceutical interventions, it uses statistical methods that can in principle establish causality. The authors modeled the complex ways in which policy, behavior and the epidemic presumably interact. In particular, their model takes into account the fact that people voluntarily change their behavior in response to changes in epidemic conditions and that it’s typically around the same time that the authorities decide to implement non-pharmaceutical interventions, because they react to the same changes in epidemic conditions as the population, so if you’re not careful it’s easy to ascribe to non-pharmaceutical interventions what is really the effect of people’s voluntary behavior changes that would have occurred even in the absence of any government interventions. Again, it’s much better than most other studies I have read on the issue and the authors should be commended for at least trying to address the methodological problems I pointed out above, but I still don’t think you should buy their conclusions.

The effect sizes advertised in the abstract are pretty large but very imprecisely estimated and the rest of the paper shows that most of them are not robust to reasonable changes in the specification of the model. Their more robust finding is that mandating face masks for public-facing employees reduced the weekly growth in cases and deaths by more than 10%, which remains true in almost every specification of the model they tried, though not in all of them. Based on one of the specifications that was associated with the largest effect, they simulate a counterfactual in which face masks were nationally mandated for public-facing employees on March 14 and find that it would have reduced the cumulative number of COVID-19 deaths in the US by 34% during the first wave, but with a 90% confidence interval of 19%-47%. They are unable to estimate the effect of closing K-12 schools, but conclude that stay-at-home orders and the closure of non-essential businesses also reduced the number of cases and deaths, even though the effect is not significant in most of the specifications they tried. Even with the specification they used to define their counterfactual, they find that if no state had ordered the closure of non-essential businesses, the number of deaths would have been 40% higher by the end of May, but the 90% confidence is interval is extremely wide at 1%-97%. According to that same counterfactual, had no state issued a stay-at-home order, the number of deaths would have been somewhere between 7% lower and 50% higher.

Thus, even if you take their results at face value, I’d say this is hardly impressive. But I don’t think you should accept their results at face value, because as I plan to explain in a detailed post about this study, doing robustness checks in a more systematic way than the authors did reveals that, with the possible exception of the effect of mandating face masks for public-facing employees, everything in that paper is almost certainly just noise. Even the effect of mandating face masks for public-facing employees seems to be noise when you use weekly growth in cases instead of weekly growth in deaths as the outcome variable. Moreover, although the results when you use weekly growth in deaths are consistent with the effect being real, they are also consistent with the effect being spurious and I actually think that’s more likely, as I will argue in my forthcoming post about this study. It shouldn’t come as a surprise that even the most sophisticated pro-lockdown study falls short because, as we have seen, even a quick look at descriptive statistics is enough to convince oneself that, whatever the effect of non-pharmaceutical interventions, it can’t be huge, so any study that finds they have a massive effect is very unlikely to be correct.

Of course, as I already noted, there are also plenty of studies that find no or relatively modest effects of non-pharmaceutical interventions. (For instance, here is another study that attempts to disentangle the reduction of growth in cases that is due to policy from that due to voluntary behavior changes and finds that policy only explains 13% of the reduction in contact rate, whereas Chernozhukov et al. found that between 1/3 to 2/3 of the reduction in death growth could be attributed to policy depending on the specification of the model used.) However, they usually suffer from the same kind of methodological problems as pro-lockdown studies, so they can’t be taken seriously either. (There are many ways in which traditional econometric methods could go terribly wrong if they’re used to estimate the effect of non-pharmaceutical interventions. For more on that issue, see this paper, which goes over the problems that several widely used designs are likely to face in that context, as well as this paper, which uses simulations to show that most econometric methods used to estimate the effect of non-pharmaceutical interventions can easily produce very misleading results.) It doesn’t mean that all this confusion is completely uninformative though. On the contrary, like the fact that it’s impossible to detect any clear effect of non-pharmaceutical interventions by inspecting descriptive statistics, the fact that the literature on the effect of those interventions contains such inconsistent results is evidence that, whatever the real effect of non-pharmaceutical interventions, it’s not very large. Indeed, if non-pharmaceutical interventions had a very large effect, not only would it be easier to see it by inspecting descriptive statistics, but there probably wouldn’t be such a wide range of inconsistent results in the literature.

I think that, in that respect, the comparison with the impact of vaccination will speak volumes. I predict that, after a large enough share of the population has been vaccinated, not only will it be easy to see the effect by inspecting descriptive statistics, but the literature will consistently find that vaccination has a large effect. In fact, thanks to the fact that Israel has already vaccinated a large share of its population (including the vast majority of people over 60), we can already see that. Here is a graph from a recent paper that analyzed the data from Israel:

This graph doesn’t involve any fancy statistical technique, it simply disaggregates based on age for a variety of outcomes, but the effect of vaccination couldn’t be clearer. Moreover, as the authors of that paper note, the same pattern wasn’t observed after the second lockdown, so we can be pretty confident this is the effect of vaccination.

Recent data from the US, where vaccination started in December, show a similar pattern:

Now this is what a very large effect looks like and the contrast with non-pharmaceutical interventions couldn’t be more striking.

A question that often comes up when I present my theory is, if I’m right and most of the reduction in transmission results from voluntary behavior changes in response to changes in epidemic conditions, then how come everywhere the authorities are putting in place strict lockdowns and other stringent restrictions to reduce transmission. First, as I hope to have demonstrated, it’s simply false that governments are doing this everywhere. It’s just that, because of the bias in the way the media reports information about the pandemic, a lot of people don’t know that many places have eschewed the use of stringent restrictions for months and sometimes have never resorted to them at all. But I think I can also explain what’s happening in places where the authorities did put in place stringent restrictions. The epidemic quickly receded during the first wave after most places locked down, following China’s example in Wuhan, which convinced people that lockdowns were very effective because the post hoc ergo propter hoc fallacy is very natural. It did not matter that so-called “lockdowns” were far more relaxed in some places than in others and that it didn’t result in any obvious differences in the trajectory of the epidemic, let alone that incidence also declined quickly in Sweden where there was no lockdown at all. Moreover, for reasons I’m not going to speculate about, people really like to think that governments have control over the epidemic, so after the first wave the idea that any difference in outcomes had to be the result of policy differences quickly became received wisdom among commentators.

Now that it has become deeply ingrained in their minds, every time the epidemic starts blowing up again, the people in charge, who undoubtedly share that belief but are more reluctant to implement very stringent restrictions precisely because they are in charge and therefore perceive more clearly the social and economic consequences, find themselves under enormous pressure from the media to lock down. In most cases, they eventually give in, after which the epidemic starts to recede. As we have seen, this would also have happened even if there had been no lockdown and indeed that’s what happened in places that didn’t lock down, but it doesn’t matter because confirmation bias is a powerful drug. Post hoc ergo propter hoc! Again, the epidemic might have started to recede a bit later and it might have receded a bit more slowly, I’m not saying that lockdowns and stringent restrictions have no effect, but the difference would not have been huge and more importantly it wouldn’t have justified the cost of restrictions. Which brings me to the last topic I want to address in this post, namely how good lockdowns and other stringent restrictions look from a cost-benefit perspective.

Lockdowns and other stringent restrictions don’t pass a cost-benefit test

I don’t claim to be doing a rigorous cost-benefit analysis here. This is already a long post and, in order to be done properly, this exercise would require another, equally long post. But lockdowns and other stringent restrictions make so little sense from a cost-benefit perspective that I don’t even think it’s necessary, because a back-of-the-envelope calculation is sufficient to convince oneself that, unless one makes completely extravagant assumptions, their costs far outweigh their benefits. I will use Sweden as a case-study because it has become the standard-bearer of a more liberal mitigation policy, even though as we have seen many places, including some that locked down during the first wave, now have even fewer restrictions in place. However, after reading this, you should be able to easily do a similar back-of-the-envelope calculation about your own country or indeed any place you want. As we have seen, it looks as though Sweden might be at the beginning of a third wave, so if incidence continues to increase you can be certain that people both inside and outside the country will start clamoring for a lockdown. I’m going to argue that, despite what pro-lockdown advocates will say if this comes to pass, a lockdown or more stringent restrictions would make no sense from a cost-benefit perspective. In fact, it’s likely that Sweden should relax some restrictions, but in any case it should definitely not imitate countries like the UK, where a very strict lockdown has been in place since the beginning of the year. The same kind of calculation would show that countries such as the UK, where stringent restrictions are currently in place, should immediately start to lift them, because their costs far outweigh their benefits.

So far about 13,000 deaths have been attributed to COVID-19 in Sweden, though excess mortality since the beginning of the pandemic is a bit less than that. For the purpose of this cost-benefit analysis, I will assume that a lockdown in place for 2 months, followed by a gradual reopening over the next 2 months (similar to what the UK is doing), would save 15,000 lives during that period. To be clear, this assumption is completely absurd, no reasonable person should take it seriously. To give you a sense of how absurd it is, you just need to know that only ~13,000 deaths have been attributed to COVID-19 in Sweden during the past 12 months and excess mortality is actually less than that, so in effect I’m assuming that a lockdown would save more lives in 4 months than the total number of COVID-19 deaths since the beginning of the pandemic, even though Sweden never locked down. Moreover, although the process is absurdly slow as in the rest of the EU, vaccination has already started in Sweden and 80% of people in elderly care homes — where about half of COVID-19 deaths took place in 2020 — have already received their first shot, so we have every reason to believe that COVID-19 mortality will be considerably less in the months ahead even if as many people get infected as during the first wave, which is very unlikely given that the prevalence of immunity is much higher and that the population is no longer naive. As we have seen, it’s impossible to estimate precisely how many lives a lockdown would actually save, but there can be no doubt that it would be far less than that. Indeed, even if Sweden doesn’t lockdown, I would be amazed if there were half that number of COVID-19 deaths in the next 4 months, but a lockdown wouldn’t save all of them and it probably wouldn’t even save half of them.

People who die of COVID-19 tend to be very old and this seems to be even more true in Sweden than elsewhere. Indeed, as of February 21, 91.3% of people who died of COVID-19 in Sweden were 70 and over. In order to do a cost-benefit analysis, even a very rudimentary one as I’m trying to do here, we need to know how long the people who die of COVID-19 would have gone on to live if they hadn’t been infected by SARS-CoV-2. This recently published study estimates that COVID-19 victims lost on average 9.8 years of life in Sweden. (The authors don’t give that figure in the paper, but it’s easy to calculate based on table S3 in the supplementary information, which gives the number of COVID-19 deaths and the years of life lost per 100,000 by country.) However, this is at best an upper bound, because this estimate was obtained by assuming that people who died of COVID-19 had the same life expectancy conditional on their age and sex as people of the same age and sex in general. Of course, this is not true, people who die of COVID-19 tend to be in poorer health and their life expectancy conditional on age and sex is therefore lower. Thus, the actual number is no doubt significantly lower, though impossible to estimate precisely. Nevertheless, since I want to be as conservative as possible, I will assume that people who die of COVID-19 in Sweden lose on average 10 years of life. Combined with the ridiculous assumption I made about the number of lives a lockdown would save, I’m really stacking the deck in favor of lockdowns and other stringent restrictions. The assumptions I made so far imply that a lockdown would save 150,000 years of life in Sweden during the next 4 months, far more than the ~130,000 years of life that have been lost in that country in the past 12 months, under the same assumption about the average years of life lost by COVID-19 death.

It remains to discuss the costs that a lockdown would have during that period. When you talk about the costs of lockdowns and other stringent restrictions, people immediately think about the economic consequences. However, while I think the economic consequences of lockdowns and other stringent restrictions are likely to be significant in the long term (despite many ridiculous arguments to the contrary that would deserve another post), you don’t even have to consider them in order to convince yourself that such a policy doesn’t pass a cost-benefit test. So rather than making highly uncertain assumptions about the long-term economic consequences of lockdowns and other stringent restrictions, I’m only going to consider the immediate effect that restrictions have on people’s well-being. Indeed, while they are in place, restrictions reduce people’s well-being because they prevent them from doing many things they would like to do. Obviously, even in the absence of a lockdown, many people wouldn’t be able to live normally, but it would take a lot of bad faith to deny that, relative to life in Sweden under the current restrictions, life in the UK or even France where there is no lockdown but a curfew at 6pm and bars and restaurants have been closed since October really sucks.

One of the weirdest things about the cost-benefit debate on restrictions, beside the fact that it’s almost non-existent, is that almost everyone talks as if restrictions didn’t have an immediate effect on people’s well-being in addition to whatever economic consequences they have. Only a handful of cost-benefit analyses of COVID-19 restrictions have been published and, to my knowledge, not a single one of them has taken into account the contemporary effect of restrictions on people’s well-being. For instance, this recently published study whose authors conclude that a 4-week lockdown in February would have been cost-effective in the US only takes into account the short-term economic cost of such a policy, but totally ignores the immediate effect on people’s well-being. (She also makes the ridiculous assumption that, in the absence of a lockdown, the epidemic would continue its course as predicted by a SIR model with constant contact rate that includes vaccination, while a lockdown would immediately push R to 0.62. This is the kind of nonsense people are talking about when they claim that lockdowns and other stringent restrictions are scientifically proven means of fighting the pandemic.) What I want to do is compute the upper bound of the immediate effect a lockdown would have on people’s well-being in order for the benefits of that policy to outweigh the cost.

This is a very straightforward calculation and you could easily do the same thing for other places. In the case of Sweden, since we have assumed that a 2-month lockdown followed by a gradual reopening over another period of 2 months would save 150,000 years of life over 4 months and Sweden has a population of 10.2 million, a lockdown would have to reduce people’s well-being by at most 150,000 / (10,200,000 * 4 / 12) = 4.5%. In other words, you would have to assume that, in exchange for not being locked down in the way people in the UK currently are but instead living under the same kind of restrictions they currently are (i. e. being able to go to a bar or a restaurant even if the sale of alcohol is prohibited after 8pm, to meet anyone they want whenever they want, to put their children under 16 in school, to go to the gym, see their colleagues at least some of the time, etc.), people would not be willing to lose about 5 days and a half during the next 4 months. It would be kind of tricky to elicit people’s preferences on the subject, though it shouldn’t be impossible. On the one hand, you’d have to make sure their answer doesn’t take into account their preferences for reducing the spread of the virus, because we’re asking them in order to estimate what impact a lockdown would have on their well-being independently of what they expect the benefits of that policy to be on reducing the spread. Indeed, we are already taking into account the expected benefits of a lockdown on transmission, so doing that would amount to a form of double counting. On the other hand, we can’t ask them to imagine there is no pandemic when they answer the question, because there is a pandemic and it means that people wouldn’t be able to benefit from their freedom as much as usual.

Nevertheless, I have no doubt that on average people would be willing to sacrifice more than 5 days and a half during the next 4 months to enjoy that kind of freedom, rather than live under the kind of restrictions people in the UK have to deal with. Moreover, keep in mind that, in order to estimate this upper bound of the reduction of well-being caused by a lockdown, I have made preposterous assumptions about how many years of life a lockdown would have. If we assume that a lockdown would only save 5,000 lives and that the average years of life lost per COVID-19 death is 7.5 years, which in my opinion are still overestimates (5,000 is approximately the total number of deaths in Sweden during the first wave, when the population was behaviorally naive, nobody had acquired immunity through natural infection and vaccination was not ongoing), it would have to be the case that a lockdown would at most reduce people’s well-being by ~1.1% on average over the next 4 months. In other words, for a lockdown to pass a cost-benefit test under those assumptions, you’d have to assume that on average people in Sweden would not be willing to sacrifice more than ~32 hours in the next 4 months to continue to live the semi-normal life they currently enjoy instead of being locked down. Given my lifestyle, I’m pretty sure that I’m one of the people who has the least hard time dealing with restrictions, but even I would sacrifice more than that. This is just absurd and I would have a hard time believing that someone who insists this actually makes sense is arguing in good faith.

If you assume that, compared to the current level of restrictions in Sweden, a British-style lockdown would reduce people’s well-being by 10% on average over a period of 4 months and make the more reasonable though still unrealistic assumptions I just made about the number of years of life that a lockdown would save, it follows that its costs would exceed its benefits by a factor of 9. Of course, this cost-benefit analysis is little more than a back-of-the envelope calculation, but I think the results are so lopsided that it’s more than enough to convince oneself that even a rigorous cost-benefit analysis would not vindicate lockdowns and other stringent restrictions. It’s true that, on the benefits side of the ledger, I have only taken into account years of life lost that a lockdown could prevent. But the virus has costs even for people who survive infection, especially those who developed a severe form of the illness. But despite the hysteria about “long COVID”, if you make realistic hypotheses, the consequences for survivors are only going to be second-order effects relative to the years of life lost by the people who died. (There would be a lot to say about the literature on “long COVID”, which makes the literature on the effect of non-pharmaceutical interventions look like the pinnacle of science, but I guess it will be for another time.) For instance, in Sweden, only 5,252 people had been admitted to ICU for COVID-19 as of February 24. Even if you assume that it reduced their well-being by 50% for a whole year, the equivalent in years of life lost is only ~3% of the years of life lost by the people who died of COVID-19 since the beginning of the pandemic when you assume 7.5 years of life lost by COVID-19 death, which is negligible.

But I have also ignored a lot of things on the costs side of the ledger, since I have only taken into account the immediate effect of restrictions on people’s well-being, which most people don’t even think about when they talk about the cost-benefit aspect of the debate on lockdowns and other stringent restrictions. In fact, I have no doubt that the economic consequences of lockdowns alone dwarf the effects of COVID-19 on people who survive, despite the ridiculous slogan that “lockdowns don’t destroy the economy, the virus does”, which is constantly recited like a mantra by pro-lockdown advocates. It would take a whole post to properly address the issue, which I may write eventually, so I will just point out that while obviously the virus alone is doing a lot of damage to the economy, it’s very silly to deny that restrictions also don’t have a large effect. In fact, even the handful of cost-benefit analyses of lockdowns that have been published, such as the one I mentioned above, assume that lockdowns have a large economic cost. People commit all sorts of fallacies when they talk about this, such as making international GDP comparison based on data that can’t be compared, citing a study that only used data on the first wave to draw conclusions about what should be done now even though the effect of the pandemic on behavior became starkly different after that or using a study that compared Sweden to other Scandinavian countries, where lockdowns were relatively mild and short compared to the rest of Europe, to conclude that very strict lockdowns would not do much economic damage above and beyond what the pandemic itself would cause.

But the central problem seems to be that people who claim there is no trade-off between economic and health outcomes don’t seem to understand that whether it’s true crucially depends on the context. If you have managed to bring incidence down to a very low level and that you can keep it there, as some countries have somehow managed to do, then it’s probably true that doing so is the best way to protect both people’s health and the economy. But this fact is completely irrelevant when arguing that countries such as Sweden, France or the US should lock down now, because the reality is that unlike the countries cited in example by the people who claim there is no trade-off between economic and health outcomes, they have not managed to keep incidence low and it’s currently very high in all of them. But when incidence is high, there is no question that bringing it down is very costly, so the fact that localized, short lockdowns whenever a cluster appears somewhere might be the optimal policy when you have managed to suppress the virus is completely beside the point. It’s a bit as if people had told Hitler in April 1945 that, in order to repel the Soviet attack, the best strategy would be to throw 50 armored divisions at Zhukov’s army. Well, sure, this sounds like a great idea, except for the fact that by then Hitler didn’t have any armored division, let alone 50 of them, to throw at Zhukov. So while this argument about the absence of a health-economy trade-off might have been convincing in Europe last Summer, when incidence was very low, it’s completely irrelevant now. In fact, I don’t even think it would have been convincing then, because I don’t think Europe or the US could plausibly have managed to keep incidence very low, but I’ll discuss this below.

In addition to the effect they have on the economy, I have ignored many other costs of lockdowns. For instance, data recently came out in France about cancer diagnoses, which show they have fallen by more than 23% in 2020 compared to the previous year. Of course, not all of the people who failed to get diagnosed in time will die and for some being diagnosed in time would not have prolonged their life much, but we’re still talking about ~93,000 missing diagnoses and it seems that it could result in between 3,000 and 24,000 excess deaths in the years to come. However, not only is it difficult to estimate what this means in terms of years of life lost, but presumably not all of those missing diagnoses are due to lockdowns. In Italy, recently published data show that the lethality of heart attack, which is a major cause of death, tripled in 2020. Again, some of that increase would no doubt have occurred even in the absence of a lockdown and it’s difficult to estimate how many years of life were lost because of that, but surely lockdowns caused some deaths. On the other hand, they probably reduced the number of deaths for some other causes, such as traffic accident fatalities, although we’re talking about pretty small numbers. Lockdowns and other restrictions may also have prevented deaths caused by other respiratory viruses, though just as for the effect of the spread of SARS-CoV-2, it’s hard to disentangle what is due to non-pharmaceutical interventions and what is due to voluntary behavior changes. My guess is that, setting aside COVID-19 deaths, lockdowns actually caused some excess deaths, but I have no doubt that all of that is dwarfed by the years of life lost because of COVID-19 deaths.

Once you take into account COVID-19 deaths and the effect lockdowns and other stringent restrictions had on them, their effect on mortality is almost certainly positive (i. e. they reduced excess mortality), but as I have argued above it’s nowhere as large as pro-lockdown advocates claim and the effect they have on people’s well-being alone is enough to make them completely irrational from a cost-benefit perspective. Again, this is true even when you ignore the economic consequences of restrictions, which likely dwarves every other thing I didn’t take into account. If you think I’m wrong, it’s not enough to say that you disagree with any particular assumption I have made, you have to show that, had I made other assumptions that you consider more plausible, the conclusion would have been different. Honestly, I don’t believe for a moment that it’s possible without making completely unrealistic assumptions, but you can always try. The truth is that I’m not even sure that lockdowns and other stringent restrictions would pass a cost-benefit if you ignored everything I said in the first part of this essay and assumed that, in the absence of a lockdown, incidence would increase quasi-exponentially until the herd immunity threshold is reached in a few weeks. But it doesn’t really matter because, even though many people continue to insist this is true, the evidence against this claim is completely overwhelming and making it today should be disqualifying. Moreover, it’s important to note that, despite what many people claimed when preliminary results showing the vaccines are highly effective were announced, the availability of vaccines didn’t change the fact that lockdowns and other stringent restrictions don’t pass a cost-benefit test. Indeed, nowhere in my argument do I assume that, if the costs outweigh the benefits, it’s because restrictions only save lives temporarily because they merely delay the inevitable. Stringent restrictions didn’t pass a cost-benefit test before we knew that vaccines would soon be available and still didn’t after we learned that for sure.

I know that many people who find the principle of such a cost-benefit analysis itself absurd on the grounds that “even a single life has no price”, but this is just a slogan and nobody really believes that. To convince you of this, imagine that a demon told us that, unless we agree to lock down the entire world for 10 years, he will kill one person at random. It’s obvious that no one but a handful of lunatics would accept this deal. Of course, if the demon told us that he was going to kill more people or that in order to avoid this we wouldn’t have to agree to lock down the entire world but only some parts of it and for less than 10 years, then depending on the details you might determine that it would be worth it. But this thought experiment shows that, even if you are one of those people who say that “even a single life has no price”, you don’t really believe that when you say it. There comes a point when the cost becomes large enough that you are willing to sacrifice lives. If this weren’t the case, life would be impossible because everything, including the most trivial activities, has a non-zero risk for you and others. Once you accept this principle, you accept the logic of a cost-benefit analysis. Of course, no one is saying that it’s easy to carry out, that’s a separate question. On the contrary, everybody who is familiar with that exercise knows that it’s very difficult to do properly. But that doesn’t mean you shouldn’t try, if only because it forces you to ask yourself what assumptions you are making to guide your decisions, which can prevent you from making a huge mistake.

With the beginning of the vaccine rollout, you would have thought that calls to lock down would subside. In fact, back in the Fall (after it became clear that vaccines would soon be available), that’s exactly what pro-lockdown advocates used to say in order to sell restrictions. They were saying that, now that we knew for sure that vaccines would soon be available, lockdowns were more warranted than ever because vaccines would soon make them redundant, so we just had to hang in there and bear the restrictions for a few extra months before we could finally lift them. But instead the same people are now calling for even more restrictions and a so-called “zero COVID” strategy, which consists in bringing incidence to a low enough level with a strict lockdown, at which point most restrictions can be lifted safely and people resume a normal life because contact tracing will be able to keep it there. To be honest, I really think that some people have basically developed a bizarre addiction to restrictions at this point and that as a result they will seize any rationale to push for more of them, but nevertheless I want to discuss this so-called “zero COVID” strategy because it has become very popular among the educated class even though I think it’s completely nonsensical.

It’s very difficult to talk about the “zero COVID” strategy because, like “abolish the police”, it’s more a political slogan than a well-defined policy, so its proponents are often vague and they often don’t say the same thing. Although the lines of reasoning are not always clear, as far as I can tell, at least 3 distinct arguments in favor of a “zero COVID” strategy can be reconstructed:

1. Even putting aside the threat posed by new variants, either those that have already emerged or those that might emerge if SARS-CoV-2 continues to circulate a lot, bringing incidence back to a very low level with a lockdown and using contact tracing to keep it there is optimal from a cost-benefit perspective because, as countries such as Australia and New Zealand showed, it’s the best way to lift restrictions and resume a normal life quickly instead of the “stop and go” policy that most Western countries have adopted.

2. Because new variants such as B.1.1.7 are more transmissible, a lockdown would give us time to increase the prevalence of immunity in the population by vaccinating as many people as possible, so that when restrictions are lifted the higher R_0 will not matter because it will have been “canceled” by the higher prevalence of immunity. Even if vaccines turn out not to protect against infections by the new variants, it won’t matter because the most at-risk people will have been vaccinated and this will at least protect them against severe forms of the illness.

3. The more SARS-CoV-2 circulates, the more likely it is that new variants will emerge that evade both the immunity induced by vaccination or by natural infection with the wild type of the virus, which would bring us back to square one. By reducing circulation of the virus, a lockdown followed by contact tracing to keep incidence low will prevent such a variant from emerging and we won’t lose the benefits of all the efforts we have made so far because a new variant causes what would effectively be a new pandemic.

Those lines of reasoning are often run together by proponents of the “zero COVID” strategy, but they are distinct arguments, so I think it’s important to distinguish them. Moreover, although they are not mutually exclusive, their premises are sometimes in tension.

I will start the first argument, which predates the emergence of B.1.1.7 and the other variants that people now worry about. As I just explained, according to the proponents of the “zero COVID” strategy, the first step of that strategy consists of implementing a strict lockdown to bring incidence down to a low enough level. They claim that, with a strict lockdown, this could be done quickly. While they are careful not to commit to any specific duration in their platform, such as this statement published in several large European newspapers and signed by many scientists, they often talk about a 4-week lockdown. There reasoning seems to be that, even if you start from a relatively high level of incidence like 20,000 cases by day (which corresponds roughly to the plateau in France since the beginning of the year), assuming the generation time distribution has a mean of 4 days, a lockdown that pushes R down to 0.7 would bring incidence back to less than 2,000 cases by day in a month. At this point, still according to the proponents of the “zero COVID” strategy, contact tracing could prevent another explosion and keep incidence low, which at 20,000 cases by day is simply not possible because the number of contacts to trace would be ridiculous. This looks pretty convincing in theory, but in practice things are more complicated. I’ll go back to contact tracing later and whether it could really do what the proponents of that strategy think, but first I want to discuss the reasoning they use to argue that a short lockdown would be enough to bring incidence back to a level where contact tracing can realistically work.

The best way to see that reality doesn’t usually cooperate with that kind of simplistic calculations is to look at some examples and what better example than Australia, which the proponents of the “zero COVID” strategy like to mention every chance they get? On July 9, as incidence had been increasing again, the state of Victoria placed Melbourne on lockdown for what was supposed to be a period of 6 weeks. But here is what actually happened:

As you can see, despite the lockdown that was ordered in Melbourne at the beginning of July, incidence continued to rise for almost a month, which is yet more evidence for my theory that lockdowns aren’t always sufficient to push R below 1 because what’s really driving transmission is people’s behavior and restrictions are not very good at targeting the kind of behaviors that contribute the most to transmission. On August 2, the rules of the lockdown were tightened in Melbourne, while the rules previously in place in Melbourne were extended to the rest of the state. Pro-lockdown advocates claim that incidence fell as a result of that, but since incidence seems to have peaked sometime between July 29 and August 4, once you take into account the incubation period it’s likely that R fell below 1 before the rules were tightened. In the end, the lockdown lasted 109 days in Melbourne, even though it was originally supposed to last only 6 weeks. Even if you buy the pro-lockdown argument that it wasn’t really a lockdown until the rules were tightened on August 2 and assume that it could have been ended safely on October 1, that’s still twice as long as the 4-week that proponents of the “zero COVID” strategy are trying to sell us. Yet even at the peak of the second wave, incidence in Victoria was only ~1/4 of that in France at the beginning of the year. I could have made the same point with the example of Wuhan, where the lockdown lasted 76 days, despite being far stricter than anything that could realistically be done in the West, especially after almost a year of restrictions.

The problem with the nice little calculation that proponents of the “zero COVID” strategy make is that, even if they don’t realize it, they make a lot of assumptions that are simply not plausible. In particular, it assumes that as long as the same restrictions in place R will remain the same and in particular that it doesn’t depend on incidence, so that if a strict lockdown can bring it to 0.7 it will stay there for the whole duration of the lockdown. But in practice that’s never what happens and, if my theory is correct, there is nothing surprising about this. Again, what really drives transmission is people’s behavior and it responds to change in epidemic conditions, so when incidence falls they eventually relax and R starts rising again even if the restrictions in place are exactly the same, because restrictions only have a limited effect on the behaviors that affect transmission the most and people’s voluntary behavior matters more. (Indeed, if you look at mobility data for the UK below, you will see that mobility started to fall before the third national lockdown and that after reaching a trough it has been going up since then despite no relaxation of the rules.) Another implicit assumption of the calculation that proponents of the “zero COVID” strategy make to argue that a 4-week lockdown would be sufficient is that the generation interval will remain the same, but to the extent that a lockdown works, it’s conceivable that it could lengthen the generation interval. However, even keeping R equal, a longer generation interval results in a higher rate of growth, in which case it will also take longer than anticipated to bring incidence down to the same level. Thus, despite the simplistic calculations advertised by proponents of the “zero COVID” strategy, there is no doubt that in places where incidence is currently high it would take more than 4 weeks of lockdown to bring it back to a low enough level for contact tracing to take over.

Not only would it be harder for the US or European countries to replicate what Australia and New Zealand did because in most of them incidence is currently higher than it ever was in Australia and New Zealand, but it would also be more difficult because they are far less isolated from the rest of the world. In particular, European countries are strongly integrated with each other, with a lot of people traveling between them for economic, cultural and other reasons. Obviously, this is even more true of the US, where a lot of people travel between states. First, they would have to close their borders to each other for a long time, which given how integrated they are would have a much higher economic and human cost than in Australia and New Zealand. This couldn’t realistically last very long, but unless they all managed to suppress the virus, the virus would start to spread again as soon as they opened their borders to each other, so they would have to coordinate to implement this strategy more or less simultaneously even though the epidemic doesn’t follow the same course at the same time everywhere. I know that proponents of the “zero COVID” strategy have imagined putting in place zones between countries that have managed to suppress the virus, within which people could travel more or less freely, but even that would require a lot of coordination. This coordination problem alone, that Australia and New Zealand never had to face (which is why I think Europe couldn’t have pulled off what Australia and New Zealand did even last Summer when incidence was very low everywhere), is sufficient to make the whole project completely unrealistic, yet as we have seen it’s hardly the only obstacle. It’s the sort of nonsense that people who are totally removed from political decision-making come up with because they ignore the economic and political constraints that decision-makers face, but you just can’t wish those constraints away.

Even if all countries in Europe and states in the US somehow managed to more or less simultaneously bring incidence back to a very low level, they would have to keep it low after that. The proponents of the “zero COVID” strategy are counting on contact tracing to do the job, but it’s doubtful that it would actually work. First, it has never worked in the past to prevent another explosion of incidence anywhere in Europe or the US, so it doesn’t seem very reasonable to count on it to work the next time. You may think that it’s because we didn’t do it right before, so it doesn’t mean that it wouldn’t work if we tried again, but what makes you think that governments that have failed to implement contact tracing correctly in the past will succeed now? I’m sure you’ve heard the quote attributed to Einstein about the definition of insanity and, while I think he never actually said that, I still think it applies pretty well here. The proponents of the “zero COVID” strategy are asking that we implement a very costly lockdown, especially since as we have seen it would last much longer than they claim and may not even be enough to bring incidence where they think it would need to be in order for contact tracing to work, on the assumption that the health authorities would do better than before. I don’t know about you, but if there is one thing this pandemic didn’t do, it’s increase my confidence in the ability of the people in charge to learn from their mistakes. It’s all the more unlikely in the case that, if as the proponents of the “zero COVID” strategy insist, B.1.1.7 is really more transmissible than the wild type, which would also make contact tracing more difficult. Strangely, despite their obsession with the new variants, the proponents of that strategy apparently did not think about that.

But frankly I’m not even convinced that, if contact tracing wasn’t able to prevent incidence from exploding in the past, even in Europe last summer when incidence was very low everywhere, it’s because it was done poorly rather than because it was intrinsically very difficult to pull off. The proponents of the “zero COVID” strategy just assume that is the case, but the truth is that nobody knows. Similarly, they claim that, if most East Asian countries were able to keep incidence low, it’s because of contact tracing, but they actually have no idea. Indeed, they used to say the same thing about Germany, but we know what happened next. All they know is that most East Asian countries were able to keep incidence low without locking down and that they used some kind of contact tracing, but they don’t know that it’s because of contact tracing and in some cases I actually find that hypothesis extremely implausible. If you want to say that rich countries such as South Korea, with a well-funded health care system and high quality infrastructure, were able to keep incidence low thanks to contact tracing, that’s something I can believe. But if you tell me that’s the reason why countries such as Cambodia, Myanmar and Thailand, which have a GDP per capita that are respectively ~1/29, ~1/33 and 1/6 that of Germany, were able to contain the pandemic without lockdowns, then I don’t know what to say other than you urgently need to come back to reality. I don’t know why East Asian countries were largely spared by the pandemic, but whatever the explanation, I know that it can’t be just because of their awesome contact tracing. The fact that such a ridiculous idea has become received wisdom speaks volumes about the state of public discourse. The truth is that, compared to Western countries, many of those places did almost nothing to stop the spread of SARS-CoV-2 but were vastly more successful, so clearly there must be other factors.

Incidentally, note that Australia and New Zealand, despite having vastly more resources than Cambodia, Myanmar and Thailand, don’t trust that contact tracing alone can keep incidence low since they now lock down entire cities as soon as a few cases are detected. To be clear, I do not doubt that contact tracing can reduce transmission, but the truth is that we have very little evidence about the effect it has. As far as I know, the best we have is a very ingenious study that exploited quasi-random variation in contact tracing in England due to a data processing error (it turns out that Excel is actually good at something, even if that’s because it’s bad), but while I think it’s good evidence that contact tracing can reduce transmission and save lives, it’s hard to generalize the results beyond England and there is no way to conclude from this paper that contact tracing would be enough to keep incidence low for several months after a lockdown even in England. It’s possible that, were it not for cultural and legal constraints that limit how intrusive contact tracing can be in Western countries, it could actually keep incidence low after a lockdown. Perhaps contact tracing is actually what allowed South Korea to contain the pandemic because it didn’t face those constraints, but again we don’t actually know that and, in any case, the fact is that Western countries do face those constraints, so it wouldn’t do them any good even if that were true.

Moreover, unless the proponents of the “zero COVID” strategy propose that European countries and US states keep their borders closed to each other even after incidence has fallen to a very low level until almost everyone has been vaccinated (which in the EU at least will probably not happen until this summer at the earliest), a failure in any country or state would endanger all the others. Even if the other countries or states put the one where contact tracing failed in quarantine as soon as incidence started increasing again, given the lag between the time infections start to increase and the time it shows up in the data about tests, the exponential nature of the process in the short-run and how integrated European countries or US states are, there is a serious risk that a resurgence of the pandemic in one of them would quickly spread to the others, which may actually be part of the explanation why Europe and the US had a harder time keeping incidence low. Beside, this would also require a lot of coordination, which as we have seen would be very difficult if only for political reasons. In short, given the situation in Europe and the US at the moment, the “zero COVID” strategy is a fantasy that will never happen. Even if that were a realistic option, you could easily show by the same argument as before that it would make no sense from a cost-benefit perspective, especially since as I argue it would take a lot more than 4 weeks to reach a point where it’s safe to lift restrictions. Again, the “stop and go” policy that most Western countries are currently using is entirely self-imposed, they could lift most restrictions immediately and it would be a clearly superior option from a cost-benefit perspective. Moreover, since most at-risk people will soon have been vaccinated even in the EU (where the process is excruciatingly slow), the cost of the pandemic is about to fall dramatically, which brings me to the second argument in favor of the “zero COVID” strategy.

The argument is that, since B.1.1.7 is significantly more transmissible than the wild type and it will soon be dominant everywhere in Europe and the US, it makes sense to lock down to prevent incidence from exploding. Note that it doesn’t even follow from this argument that we should keep incidence low indefinitely but only long enough for us to vaccinate enough at-risk people, though of course if we can keep it low with contact tracing it’s even better as long as it’s not too expensive. In fact, it doesn’t even imply that incidence be pushed very low, just that it be prevented from exploding due to the more transmissible new variants. Presumably, in order to calculate the optimal number of at-risk people that should be vaccinated before restrictions are lifted, a cost-benefit analysis would have to be carried out to balance the cost of the lockdown needed to prevent incidence from exploding because of the new variants. The problem with that argument is that it assumes that lockdowns are extremely effective to reduce transmission and make a huge difference relative to a situation where few restrictions are in place but people voluntarily change their behavior in response to changes in epidemic conditions, but as we have seen the evidence doesn’t support that view. If the variants really were incredibly more transmissible than the wild type, this might still make sense, because even the modest difference that lockdowns and other stringent restrictions probably make could be what it takes to push R below 1. But I think at this point it’s perfectly clear that, despite what people initially thought and what many continue to think, the extent to which B.1.1.7 is more transmissible than the wild type has been wildly overestimated. There is clearly something different about that variant, but I don’t see how people can still maintain that it’s 70% or even 50% more transmissible than the wild type.

There are several ways to convince oneself of that. One of them is to look at epidemic data in places where B.1.1.7 has recently been spreading. For instance, according to the French government, the prevalence of B.1.1.7 was ~3.3% on January 8 and ~39.5% or ~49% during the week between February 15 and February 21, depending on whether you use full-sequencing data or data based on S-gene target failure after a PCR or antigen test. Yet here is how incidence, R and mobility have changed between January 8 and February 21:

Incidence recently started increasing again in France, but we don’t have data on the prevalence of B.1.1.7 after week 7, so I only show the data up to February 21.

As you can see, everything was basically flat during that period. If you infer effective reproduction numbers in the straightforward way from the data on incidence and the prevalence of B.1.1.7 among positive samples, depending on what assumptions you make about the generation time and whether you use full-sequencing data or data based on S-gene target failure, you find that it’s between 30% and 45% more transmissible than the wild type. However, for that inference to be correct, it would have to be the case that R has gone down significantly for the wild type during that period even though mobility was completely flat. Now, I know the data about everything are extremely low quality here and we must therefore be careful in drawing conclusions from them (in particular I think there are good reasons to think that mobility data are a very noisy measure of the behaviors that drive transmission), but I would be surprised if B.1.1.7 was more than 30% more transmissible than the wild type and I don’t see how it could be 70% more transmissible or even 50% more transmissible.

Indeed, when epidemiologists made short-term projections based on the assumption that B.1.1.7 was more transmissible than the wild type to such a large extent, they failed miserably everywhere. For instance, here is a projection made on January 29 by the Scientific Council, which advises the French government about the pandemic, based on the assumption that B.1.1.7 was 50% more transmissible than the wild type:

As you can see, both incidence and hospital admissions were supposed to start increasing exponentially at the beginning of February (you will also note that the epidemiologists who advise the French government continue to assume that people don’t voluntarily change their behavior when incidence explodes), but as we have seen it actually decreased in February until it started increasing again recently.

Another way to see that, no matter how transmissible B.1.1.7 is, the difference with the wild type can’t be as large as originally claimed is to look at curves of incidence in places where it’s dominant:

I have put the daily number of COVID-19 cases in log scale, so you can visualize the growth rate more easily. As you can see, incidence has actually been falling more rapidly after the third national lockdown than after the first, yet it wasn’t stricter and it’s doubtful that after almost a year of restrictions compliance with the rules was higher and that people’s voluntary behavioral changes were larger than during the first wave.

Indeed, if you look at mobility data, it’s clear that mobility fell dramatically more during the first national lockdown than during the third:

Now, I know that data on cases were pretty bad everywhere during the first wave and as I already noted mobility data are probably a very noisy measure of the behaviors that drive transmission, but still you’d have to be crazy to look at these curves and conclude that it’s plausible that B.1.1.7 is 50% more transmissible than the wild type.

I’m only showing the data for the UK, but to be clear, they show exactly the same thing for Ireland, Denmark and Portugal. It’s true they have all locked down recently, but since mobility didn’t fall as much as during the first wave and we know that it’s possible to deal with the wild type without a lockdown or even other stringent restrictions, I don’t see why it wouldn’t be possible to do the same with B.1.1.7. In fact, it looks as though B.1.1.7 will soon be dominant in many places that haven’t locked down and I predict that, even if incidence starts increasing again, it will eventually fall long before the herd immunity threshold is reached even if they persist in not locking down. Of course, part of the explanation is probably the fact that nobody was immune at the beginning of the first wave, whereas now the prevalence of immunity is pretty high in most places. But it would make no sense to ignore this fact, because it means that even if the variants really are more transmissible than the wild type, which they probably are to some extent, this will be alleviated by the fact that the prevalence of immunity is also higher, which lowers the effective reproduction number other things being equal. What all of this suggests is that, no matter how much more transmissible the variants of concern are relative to the wild type, they are not so much more transmissible that voluntary behavioral changes will not be able to prevent incidence from exploding until the herd immunity threshold is quickly reached. It follows that, by the same argument as before, lockdowns and other stringent restrictions would not pass a cost-benefit analysis, because it wouldn’t save enough people even if the lockdown were as short as the proponents of the “zero COVID” strategy claim it would be, which as I argued it almost certainly wouldn’t be.

The third argument in favor of that strategy frankly strikes me as completely ludicrous, which is why I kept it for last, but I will nevertheless try to make as strong a case for it as I can. In a nutshell, the argument is that, the more SARS-CoV-2 circulates, the higher the probability that a new variant that can evade currently existing immunity — whether induced by natural infection or vaccination — will emerge and take us back to square one, so we should again bring incidence back to a low enough level with a lockdown and then keep it there with contact tracing to make sure the population of SARS-CoV-2 remains small and minimize the probability that such a dangerous variant emerges. Some people who make that argument seem to suggest that we should aim at eradicating the virus globally to prevent that, but even if this eventually happens (which I seriously doubt if only because I don’t think it will be worth the trouble once enough people have been vaccinated), it will take years in the best case scenario and we obviously aren’t going to keep borders closed, lock down whole cities as soon as a few cases are detected and engage in very intrusive contact tracing for years. The virus will continue to circulate a lot in many areas of the world even if Europe and the US manage to suppress it durably within their borders and, if new variants that are able to evade immunity induced by current vaccines or natural infection by older variants of the virus are to emerge, they will emerge over there anyway and will reach Europe and the US as soon as they open their borders again. So I think a stronger version of the argument is that European countries and the US ought to suppress the virus within their borders and remain closed to parts of the world in which it’s still circulating a lot until almost everyone has been vaccinated and we have developed the production capacity and the infrastructure we need to quickly produce and distribute updated versions of the vaccine against hypothetical new variants of that sort.

This argument has the same problems as the others, but it’s even less plausible because it also has other, even more serious problems. Like the other arguments used to support the “zero COVID” strategy, it assumes that a lockdown would have a large enough effect on transmission relative to letting people’s voluntary behavioral changes drive incidence down to justify its cost, that contact tracing would actually be able to keep it there once it has reached a low enough level, that European countries and US states would be able to solve the coordination problem this strategy poses, etc. But while the other arguments in favor of that strategy were at least premised on actual threats, this argument says that we should try to pull off this strategy, which again has a very low probability of working and would have a very large cost even if by chance it turned out to work, as prophylaxis against variants that as far as we know don’t even exist yet and for all we know may never exist. Indeed, according to the best evidence we have, immunity induced by current vaccines or natural infection by older variants of the virus will probably work against the variants of concern that we currently know about. At least, experts seem pretty confident that it will at least protect against severe forms of the disease in the vast majority of cases, which is what really matters. Again, I think most restrictions are not justified at this point, but to the extent they are, it’s because of severe disease. Once the virus no longer causes severe illness, it will be even less sensible to have restrictions in place than it already is.

It’s true that neutralizing antibodies induced by current vaccines or natural infection by older variants seem to be less effective against B1.351, though not against B.1.1.7, but neutralizing antibodies are just one part of the immune response against SARS-CoV-2 and it seems that both natural infection by the wild type and Moderna and Pfizer’s vaccines elicit a strong T-cell response against B.1.1.7, B1.351 and P.1. (This had already been shown by another study for immunity induced by natural infection and Pfizer’s vaccine against B.1.1.7 and B1.351.) This suggests that immunity induced by current vaccines and natural infection by older variants will at least protect against severe forms of the disease. People started to panic after a study found that AstraZeneca’s vaccine had very low efficacy against B1.351, but the confidence interval is so wide that the point estimate is essentially meaningless. Again, the results I mentioned previously suggest that current vaccines and natural infection by older variants will at least protect against severe forms of the disease upon contact with B1.351, which is also what preliminary data from the trial of Johnson and Johnson’s vaccine in South Africa suggest. Indeed, while the trial found that efficacy was lower in South Africa than in the US or Latin America, the effect was moderate since efficacy against moderate to severe disease was estimated to be 57% in South Africa against 66% in Latin America and 72% in the US. Moreover, according to data released by the FDA, the difference is not even statistically significant. In any case, according to Johnson and Johnson, efficacy is 85% against severe disease across regions, which suggests that vaccines will be able to prevent hospitalization and death against not only B1.351 but also P.1. Moreover, the evidence so far doesn’t suggest that either B1.351 or P.1 is intrinsically more transmissible than the wild type, so we have no reason to think they will spread like B1.1.7, against which current vaccines seem to be very effective.

So despite all the scaremongering about variants, everything indicates that once at-risk people are vaccinated, SARS-CoV-2 will no longer cause severe illness except rarely. Eventually, new variants may emerge that evade even T-cell response induced by current vaccines and infection by older variants, but there is no reason to think it will happen before we have the capacity to quickly update the vaccines and distribute them to a large share of the population. Pfizer and Moderna have already said they had started to work on boosters to strengthen immunity against B1.351. Thus, we should continue to monitor new variants of SARS-CoV-2 closely and make the necessary investments to build this capacity, but it’s completely insane to embark on a probably futile and undoubtedly extremely costly effort to eradicate the virus in Europe or the US as prophylaxis against merely hypothetical threats. It seems that, with that line of reasoning, you could argue that we should remain locked down indefinitely to minimize the risk that a dangerous variant of one of the more than 200 other respiratory viruses currently in circulation will emerge. Of course, they’ve been around for a much longer time so they’ve had more time to explore the evolutionary landscape and they don’t individually circulate as much as SARS-CoV-2 because human populations are no longer immunologically naive to them and they have become endemic a long time ago, but again there are more than 200 of them so I don’t see how you can say that the risk is not at least as high. This fact alone, on top of everything else, should be a reductio of that argument in favor of the “zero COVID” strategy.

Conclusion

A lot of people seem to overestimate the impact of lockdowns and other stringent restrictions. Again, I’m not saying they have no effect, but the effect doesn’t seem to be as dramatic as many people claim and, in particular, it’s simply not the case that, unless a country lock down when incidence starts increasing, it will continue to increase exponentially until the herd immunity threshold is quickly reached. As I have argued, it seems that people voluntarily change their behavior so as to prevent that long before that point is reached, even in the absence of stringent restrictions. Meanwhile, lockdowns and other stringent restrictions seem to be very blunt instruments, which have a hard time targeting the behaviors that affect transmission the most. This is probably why they don’t seem to work very well as long as incidence is low and people are not scared, which in turn explains why R often doesn’t immediately fall after a lockdown and why it climbs back up even while the restrictions are still in place when incidence has fallen to a low enough level. It’s true that many studies have found that restrictions have had a very large effect, but as I have explained, they are not credible in view of what descriptive statistics show and because their methods are generally unreliable, sometimes laughably so.

Not only do pro-lockdown advocates dramatically overestimate the effect of restrictions, but they seem to care about health outcomes to the exclusion of almost everything else. In particular, they are overly concerned about the threat of overwhelming hospitals, while not caring enough about the costs that restrictions impose on the population. Of course, it’s bad to overwhelm hospitals, but so is depriving kids of a normal childhood by preventing them from attending school in-person or socializing with their friends, closing small businesses that may keep productivity low but have large positive externalities for local communities, impoverishing students and ruining their mental health because the kind of businesses where they traditionally find jobs to support themselves have been forced to close and they aren’t able to socialize anymore, etc. When you point out those kinds of consequences, pro-lockdown advocates are quick to retort that governments could do a better job at alleviating them and in many cases they are even right, but the reality is that political constraints can’t be wished away and they often prevent that.

As I have argued above, even when you make preposterous assumptions, lockdowns and other stringent restrictions don’t pass a cost-benefit test even right now when relatively few at-risk people have been vaccinated, so this is only going to become more true as the vaccine rollout continues and picks up the pace. Even a quick and dirty cost-benefit analysis is enough to convince oneself that the costs of stringent restrictions outweigh their benefits by such a huge margin that only collective hysteria can explain why so many people continue to support those absurd policies. Not only would societies as a whole be much closer to the optimum from a cost-benefit perspective if we immediately started to lift stringent restrictions, but many people individually could improve their well-being by not refraining from certain activities that don’t seem to have a large impact on transmission, which they don’t realize because of all the scaremongering. Unfortunately, not only are pro-lockdown advocates not learning from our past experience, but many of them are doubling down with the so-called “zero COVID” policy, which is even more ridiculous from a cost-benefit perspective than less radical pro-lockdown stances. The proponents of that strategy clearly haven’t considered the costs their policy would have, the obstacles it would face and the benefits it would bring compared to more liberal policies. If they had, they wouldn’t suggest that we embark on such a project to address threats we actually face, let alone hypothetical threats such as variants capable of completely evading currently existing immunity.

Even though many governments around the world have been abolishing many of the individual freedoms traditionally enjoyed by their populations for months, as far as I know, not a single one of them has published a cost-benefit analysis to justify this policy, even though it’s something they routinely have to do in order to make far less consequential decisions. Even if you think that restrictions are justified, this should be very concerning to you and you should be clamoring for such a cost-benefit analysis to be published. I don’t think I’m being unreasonable when I say that, if governments need to publish a cost-benefit analysis before they build a bridge, they should also have to publish one before they abolish the basic freedoms of millions of people for months. I can understand why this wasn’t possible during the first wave, when everyone was taken by surprise (which incidentally was already a huge failure, but that’s another story), but now they’ve had months to do it and it doesn’t seem to have even occurred to them. Many governments have committed the most radical violations of human rights in the West since the end of WW2, not because doing so is justified by sound epidemiological and moral reasoning, but rather because they are playing it by ear and have fallen prey to the hysteria that has taken over both the media and the experts that advise them. Indeed, let’s not forget about the role played by parts of the scientific community in that debacle, which have been fueling the hysteria in question with studies that sometimes are so bad they come very close to scientific fraud. I’m convinced that eventually it will be widely acknowledged that we overreacted, but a lot of damage has already been done and I fear that, by the time enough people wake up, even more will have been done.