It is well known that the evolutionary dynamics of RNA viruses, including influenza, dengue, and norovirus, occur on the same timescale as their ecological dynamics. Models that focus on understanding the ecological dynamics of these viruses therefore need to integrate appropriate models for their evolution; similarly, models that focus on understanding the evolutionary dynamics of viruses need to integrate appropriate models for the ecological interactions that give rise to accurate herd immunity profiles of the host population. In the last decade, many models have been formulated that have integrated both the ecological and the evolutionary dynamics of viral pathogens. However, most of these are either individual-based models, or models that, although mathematical in form, assume an artificially constrained subset of viral strains. Furthermore, most theoretical models to explain the evolutionary dynamics of viral pathogens have focused exclusively on a single host-pathogen system. A comparative approach to address the dynamical differences between several host-pathogen systems would provide a significant improvement in our understanding of viral dynamics.  

Results/Conclusions

Here, we introduce a simple two-tiered model for viral pathogens that greatly reduces the complexity of simulations for antigenically variable pathogens. The first tier models the ecological dynamics of viral variants by simulating patterns of antigenic turnover. The second tier models the evolutionary dynamics of the virus’s genetic sequences. Separation of the model into these two subcomponents allows for a much simpler simulation of both the ecological and the evolutionary dynamics of the virus. Different parameterizations of the model can result in different ecological dynamics and different phylogenetic tree topologies. We then use this model to explore the reason for the dynamical differences between the three variants of flu currently circulating in humans: influenza A (H3N2), influenza A (H1N1), and influenza B. We find that the ecological and evolutionary dynamics of these three variants are best explained by a model that incorporates both gradual and punctuated antigenic evolution. Furthermore, we show that the variants’ characteristic dynamical differences can result solely from differences in their transmission rates and mutation rates. We end with a discussion of the microevolutionary processes that underlie the antigenic turnover patterns of flu and how these processes shape the virus’s long-term dynamics.