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. 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. 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.
Philippe Lemoine
Interesting study about a conundrum that has puzzled many since the start of the pandemic, yet few have offered plausible solutions: why does transmission fluctuate so much even in the absence of clear measures or changes in human behavior? There are multiple examples for this, and the author mentions some of the more known, such as Florida and the Indian Delta wave, which subsided almost as abruptly as it started. The recent surge in Romania has also ended relatively fast, despite scarce measures from the authorities – as before, I mostly attribute these swings to schools openings, and the current reduction in cases comes after schools were closed again all over the country.