Dynamic behavior of a stochastic SIQS epidemic model with Lévy jumps

In this paper, we propose a stochastic SIQS epidemic model with Levy jumps and investigate sufficient conditions of the extinction and persistence of the disease. Then, we analyze the asymptotic behavior of the solution of the model around the endemic equilibrium of the corresponding deterministic model. We find that Levy jumps can suppress the disease outbreak. Numerical simulations are carried out and approve our results.