Analysis of a stochastic epidemic system with quarantine and perturbation

The global stability of the endemic equilibrium of the epidemic system introduced by Herbert is investigated firstly. Subsequently, we consider the stochastic system by adding the perturbations. The perturbations play an important role in changing the properties of the epidemic system. We get the conclusions that the strong noises can make disease go extinct, and the stationary distribution will exists when conditions in Theorem 7 in this paper hold. Numerical simulations are carried out to confirm the analytical results.