Have we been thinking about the pandemic wrong? The effect of population structure on transmission

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.

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