Dynamical Behaviors Of Stochastic Multi-Group SIS Epidemic Models

In this paper, we consider the dynamic behaviors of SIS models with contact ratio perturbation by Lyapunov analysis method. Firstly, we show the existence unique positive solution of the stochastic systems. Secondly we investigate the extinction of the systems and reveal that the large noise results in the extinction of the species.Thirdly, we investigate the persistence and non-persistence of the systems. Moreover,we discuss the asymptotic behavior of the stochastic systems near the disease free equilibrium point and disease equilibrium of corresponding deterministic system respectively, point out that the stochastic systems have the similar properties with those of the corresponding deterministic systems under small noise, and yield the persistence in the time average. Finally, we obtain the existence of stationary distributions.