Summary: In this paper, we extend the classical susceptible-infected-recovered (SIRS) epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation. We prove the global existence of unique solution. Using the Lyapunov method, we find sufficient conditions for the stochastic asymptotic stability of equilibrium solutions of this model.
Finally, establish the existence of a unique ergodic stationary distribution and illustrate our results.