Stability of a stochastic discrete SIS epidemic model with general nonlinear incidence rate

Abstract

The purpose of this paper is to study the stability of a stochastic discrete SIS epidemic model with a general nonlinear incidence rate at the equilibrium. Based on a continuous SIS model with stochastic white noise directly proportional to the deviation of the state from the equilibrium, the model is discretized by the Euler–Marryama method, and then the stochastic discrete SIS epidemic model is obtained. A sufficient condition for the stability in probability of the nonlinear difference equations with stochastic perturbations at the equilibriums is proposed. The sufficient conditions for the stochastic stability of the model at positive equilibrium and boundary equilibrium are obtained. Numerical simulations show the influence of noise intensity on the stability of stochastic discrete model.