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 ℜ 0 of the model is calculated. It is proven that the disease-free equilibrium is locally asymptotically stable if ℜ 0 < 1 and globally asymptotically stable for some additional conditions, and the endemic equilibrium is locally asymptotically stable if ℜ 0 > 1. Numerical simulations are presented to illustrate the stability results, and the sensitivity analysis of the basic reproduction number ℜ 0 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 ℜ 0 . [ABSTRACT FROM AUTHOR]