Qualitative analysis of a nonautonomous stochastic SIS epidemic model with Le´vy jumps.

In this paper, we study a nonautonomous stochastic SIS epidemic model with Le´vy jumps. We first establish that this model has a unique global positive solution with the positive initial condition. Then, we investigate the condition for extinction of the disease. Moreover, by constructing suitable stochastic Lyapunov function, sufficient conditions for persistence and existence of Nontrivial T-periodic solution of system are obtained. Finally, numerical simulations are also presented to illustrate the main results.