Eco-evolutionary stable strategies of antigenically escaping viruses

Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2, promoting diversity in the viral population and leading to repeated epidemics and reinfections. This antigenic evolution is sustained by continuous pathogen transmission between hosts and is fueled by remarkably high viral mutation rates. While high mutation rates clearly promote antigenic escape, they also induce a large mutational load, reducing viral fitness. In this context, it remains unclear how the immune pressure exerted by a population of hosts drives the evolution of these viral strategies. To tackle this question we model the co-evolution between finite population of hosts and viruses in a one dimensional antigenic space whose metric describes the cross-reactivity between viral variants and antibodies generated by previous infections. We observe that the antigenic evolution induced by the immune pressure is characterized by a traveling wave of adaptation whose speed and size are primarily ruled by the efficiency of cross-reactive immunity. As a consequence, we show that the evolutionary stable viral strategy is dictated by a trade-off between maximizing the speed of antigenic evolution when the cross-reactivity is small and maximizing the reproduction ratio when it is larger. In particular, this result implies that a small cross-reactivity favors the evolution of highly transmissible and deadly viruses with mutation rates close to the extinction threshold.