Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and Levy Jumps

摘要

A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0 1,it fluctuates around the endemic equilibrium of the deterministic model.