An stochastic sirs model with nonlinear incidence rate and transfer from infectious to susceptible

In this paper, we studied that asymptotic behaviors of an stochastic SIRS model with nonlinear incidence rate and transfer from infectious to susceptible. First of all, we given the global existence and positivity of the solutions. Moreover, we found that stochastic perturbation in the environment can lead the disease to extinction under certain conditions. Furthermore, we established that sufficient conditions for the existence of a stationary probability measure of the model. Finally, we made a brief conclusion.