Stability analysis of a discrete SIRS epidemic model with vaccination

A discrete SIRS epidemic model with vaccination and a general infection probability function is investigated in this paper. The basic reproduction number of the model is calculated. It is proven that the disease-free equilibrium is locally asymptotically stable if and globally asymptotically stable for some additional conditions, and the endemic equilibrium is locally asymptotically stable if . Numerical simulations are presented to illustrate the stability results, and the sensitivity analysis of the basic reproduction number shows that the proportionality coefficient of unvaccinated susceptible, the probability that infected individuals do not recover, and the probability of survival have much more effect on .