A simplified model of the evolution of the first step escape mutant (I^∗) using an SIR model framework.

The transmission rate $\beta$ to susceptible individuals and the clearance rate $\kappa$ are assumed to be equal for both variants. Only the escape mutant is partially able to infect resistant individuals (at a rate reduced by a factor p relative to the rate of infecting susceptible individuals). The model considers only the first step in the accumulation of mutations that increase the ability to reinfect otherwise resistant individuals but could be extended to model subsequent steps by mutation.