Abstract

The evolution of viral traits is affected by different selective pressures. One trait of particular interest is viral virulence, which can be broadly defined as a measure of the harm produced by the virus to its host. How and to what extent different factors in virus-host dynamics shape virulence has been largely debated. We present a model of virus-host dynamics with the aim of studying how competition between viral particles and the immune response of the host affect virulence. The model describes, and links, the viral dynamics inside individual hosts and the dynamics of the susceptible and infected individuals in the host population. We first show that when the hosts have an adequate immune response (so that they completely recover from the infection on a short time scale), the viruses tend to increase their virulence. On the contrary, if the hosts are vulnerable (meaning that they will eventually die from the infection), low virulences will be selected. We then move to a richer scenario in which the host population is mixed and contains a fraction $p \in (0,1)$ of vulnerable individuals. We see that the selected virulence and the number of deaths caused by the virus per unit time exhibit biologically relevant behaviors as $p$ takes intermediate values.