Epidemic model with strain-dependent transmission rate

Persistent epidemic can lead to the emergence of new virus strains due to virus mutations. This work is devoted to the SIR model with strain-dependence of infected individuals due to virus mutations and a continuous strain variable. Characterization of epidemic progression is obtained for a strain-dependent infectivity function in numerical simulations and with some analytical estimates. Taking into account limited infection-induced immunity, transition from recovered to susceptible compartment is considered. Different scenarios of epidemic progression are identified. In the case of a monotonically growing transmission rate as a function of strain, only one epidemic outbreak is observed. However, if the transmission rate is a non-monotonic function, then multiple outbreaks can occur.