Stationary distribution of stochastic SIRS epidemic model with standard incidence

Abstract

We study stochastic versions of a deterministic SIRS(Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L1. This shows the system is ergodic. The presented results are demonstrated by numerical simulations.