Fig. 2: Infection dynamics, vaccination and resistance.

Susceptible individuals (x) can be infected by WT or MT virus. Infected people (y₁, y_2A and y_2B) die (at rate d) or recover (at rate a). People recovered from WT or vaccinated against WT can be infected by MT. People recovered from MT cannot be infected by WT. In our simplest model, we assume equal infectivity, recovery and death rates for both WT and MT. Vaccination occurs at rate c per day for all unvaccinated individuals (excluding those that are currently in active infection). Mutation happens (at rate μ) when exposure to a WT-infected individual (y₁) results in the generation of an MT-infected individual. Note that when exposure to a WT-infected individual (y₁) results in the generation of a WT-infected individual, the rate of infection should be multiplied by 1 − μ to conserve the sum of mutation probabilities at 1. However, since μ is small, we neglect the term 1 − μ. The rates of these events are indicated near the arrows and are used in the Gillespie algorithm implementing stochastic dynamics.