Modelling the role of immunity in reversion of viral antigenic sites

Antigenic sites in viral pathogens exhibit distinctive evolutionary dynamics due to their role in evading recognition by host immunity. Antigenic selection is known to drive higher rates of non-synonymous substitution; less well understood is why differences are observed between viruses in their propensity to mutate to a novel or previously encountered amino acid. Here, we present a model to explain patterns of antigenic reversion and forward substitution in terms of the epidemiological and molecular processes of the viral population. We develop an analytical three-strain model and extend the analysis to a multi-site model to predict characteristics of observed sequence samples. Our model provides insight into how the balance between selection to escape immunity and to maintain viability is affected by the rate of mutational input. We also show that while low probabilities of reversion may be due to either a low cost of immune escape or slowly decaying host immunity, these two scenarios can be differentiated by the frequency patterns at antigenic sites. Comparison between frequency patterns of human influenza A (H3N2) and human RSV-A suggests that the increased rates of antigenic reversion in RSV-A is due to faster decaying immunity and not higher costs of escape.