The effect of epidemiological model structure on patterns of viral diversity

Background/Question/Methods

It is well known that the epidemiological characteristics of an infection can affect the population dynamics of infectious diseases. For example, models have shown that infectious period distributions closer to normal than exponential lead to a destabilization of disease dynamics, that longer incubation periods lead to slower rates of epidemic invasion, and that transmission rate heterogeneity can impact disease emergence. Here, we instead consider how an infection’s epidemiological characteristics, and thereby its ecology, impact the evolutionary dynamics of a disease and its patterns of diversity. We specifically focus our analysis on the case of neutrally evolving RNA viruses and, using coalescent theory, illustrate how rates of genetic drift and the amount of standing genetic diversity are affected by these epidemiological characteristics. At the core of our analysis lies a general analytical approach that can be used to derive effective population sizes from the distribution of individuals’ basic reproduction numbers, and therewith rates of coalescence that determine the rate at which viral genetic diversity is lost or gained.

Results/Conclusions

We apply this general approach to four sets of common epidemiological models, with population dynamics at equilibrium. The first set is the family of SIS/SIR/SIRS models, which analytically reduce to a population genetic Moran model with the relevant population size being the number of infected individuals. The second set is the family of SIS/SIR/SIRS models with variable infectious period distributions, which transition from being a Moran model to a classic Wright-Fisher model as the number of infectious compartments increase from one to infinity. The third set is the family of SEIS/SEIR/SEIRS models, which reduce to a Moran model with a population size consisting of exposed and infected individuals. The fourth set is the family of SIS/SIR/SIRS models with individual heterogeneity in disease transmissibility, which leads to a decreased effective population size whose form can be analytically derived from the distribution of individuals’ transmission rates. We further support these analytical results through epidemiological simulations. These results have implications for interpreting effective population sizes from Bayesian Skyline Plots, for statistical inference using viral sequence data, and, ultimately, for understanding the impact that epidemiological characteristics can have on the adaptability of viruses in host populations.