A cross-immunization model for the extinction of old influenza strains

Given the frequent mutation of antigenic features, the constancy of genetic and antigenic diversity of influenza within a subtype is surprising. While the emergence of new strains and antigenic features is commonly attributed to selection by the human immune system, the mechanism that ensures the extinction of older strains remains controversial. To replicate this dynamics of replacement current models utilize mechanisms such as short-lived strain-transcending immunity, a direct competition for hosts, stochastic extinction or constrained antigenic evolution. Building on the idea of short-lived immunity we introduce a minimal model that exhibits the aforementioned dynamics of replacement. Our model relies only on competition due to an antigen specific immune-response in an unconstrained antigenic space. Furthermore the model explains the size of typical influenza epidemics as well as the tendency that new epidemics are associated with mutations of old antigens.