Stability analysis of a discrete SIRS epidemic model with vaccination

Abstract

A discrete SIRS epidemic model with vaccination and a general infection probability function is investigated in this paper. The basic reproduction number ℜ0 of the model is calculated. It is proven that the disease-free equilibrium is locally asymptotically stable if ℜ0<1 and globally asymptotically stable for some additional conditions, and the endemic equilibrium is locally asymptotically stable if ℜ0>1. Numerical simulations are presented to illustrate the stability results, and the sensitivity analysis of the basic reproduction number ℜ0 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 ℜ0.