Dynamics of a stochastic SIRS epidemic model with standard incidence and vaccination

Abstract

A stochastic SIRS epidemic model with vaccination is discussed. A new stochastic threshold Rs0 is determined. When the noise is very low (Rs0 < 1), the disease becomes extinct, and if Rs0 > 1, the disease persists. Furthermore, we show that the solution of the stochastic model oscillates around the endemic equilibrium point and the intensity of the fluctuation is proportional to the intensity of the white noise. Computer simulations are used to support our findings.