Dynamics Of Two Stochastic SIQS Epidemic Models With Lévy Jumps

In this paper,we consider two stochastic SIQS epidemic models with Lévy jumps.To begin with,we propose a stochastic SIQS model with bilinear incidence.We prove the existence and uniqueness of the global positive solution by constructing a Lyapunov function.Then we give sufficient conditions for disease extinction and persistence.In addition,we discuss the stochastic asymptotic stability at the disease-free equilibrium of the stochastic system and the asymptotic behavior at the endemic equilibrium of the deterministic model.Next,we establish a stochastic delayed SIQS system with Lévy jumps and media coverage.We still prove the existence and uniqueness of the solution.Then sufficient conditions for disease extinction and persistence are given.Finally,for the above two models,we carry out numerical simulations respectively to verify the correctness of theoretical results obtained in this paper.