Since the 1980’s, mathematical models to describe the disease dynamics of influenza viruses have focused on the incorporation of antigenic drift. The earliest models simply incorporated antigenic drift phenomenologically, through the consideration of susceptible-infected-recovered-(re)susceptible (SIRS) dynamics. A more mechanistic approach for considering antigenic drift has relied on the formulation of multi-strain models for influenza. Whether phenomenological or mechanistic in structure, however, these mathematical models have commonly assumed that antigenic drift results from postiive selection of variants with amino acid changes in epitope regions that reduce the abilility of antibodies to bind the viral hemagglutinin.
In light of an increasing body of experimental studies, however, recent work by Hensley and coauthors has recently questioned this paradigm of immune escape (Hensley et al. (2009) Science, vol. 326, pp. 734-736). In its place, the authors have suggested that the evolutionary dynamics of influenza A’s hemagglutinin (HA) protein are driven by cellular receptor binding avidity changes, and that antigenic drift is a side effect of these mutational changes.
Results/Conclusions
Here, we develop a mathematical model for the receptor binding avidity hypothesis outlined by Hensley and coauthors. The model divides hosts into different immune classes, indexed by the number of previous infections they have experienced. Consistent with viral passage data, our model assumes that a virus with high binding avidity has a selective advantage in hosts with high levels of immunity, while a virus with low avidity has an advantage in hosts with low (or no) levels of immunity. Through numerical simulation of the model, we first show how epidemiological parameters affect mean binding avidity levels and ultimately rates of antigenic drift. We then use the model to consider how vaccination policies preferentially targeting children may lower rates of antigenic drift. Finally, we explore whether (and under what epidemiological circumstances) this model is consistent with the ladderlike evolution of influenza's hemagglutinin protein.