LAUSR

The goal of this paper is to introduce and initiate a study of a stochastic SIRS epidemic model with standard incidence which is perturbed by both white and telegraph noises. We first show persistence in the mean and then establish the sufficient conditions for extinction of the disease. Moreover, in the case of persistence, we obtain sufficient conditions for the existence of positive recurrence of the solutions by means of structuring suitable stochastic Lyapunov function with regime switching. Meanwhile, the threshold between persistence in the mean and extinction of the stochastic system is also obtained. Finally, we test our theory conclusion by simulations.