Dynamics analysis of a stochastic SIRS epidemic model with nonlinear incidence rate and transfer from infectious to susceptible.

In this paper, we investigate the dynamics of a stochastic SIRS epidemic model with non-linear incidence rate and transfer from infectious to susceptible. Firstly, the existence and uniqueness of global positive solution of the model with any positive initial value are proved. Next, sufficient conditions for extinction and persistence of the disease are established. It is found that a large noise intensity has the effect of suppressing the epidemic. At last, some numerical simulations are introduced to demonstrate the theoretical results. Our results generalize and improve the existing results.