Qualitative study of a stochastic SIRS epidemic model with information intervention

In this paper, we consider a stochastic SIRS epidemic model with information intervention. First of all, the existence and uniqueness of the global positive solution are obtained. Then, we derive sufficient conditions for the extinction and persistence of the disease. Moreover, by establishing appropriate Lyapunov function, the existence of a stationary distribution is discussed. Some numerical simulations are given to illustrate our analytical results. •Stochastic SIRS epidemic model with information intervention is considered.•Existence and uniqueness of the global positive solution are obtained.•Sufficient conditions for the extinction and persistence of the disease are established.•The ergodic stationary distribution exists under certain condition.•Some numerical simulations are given.