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,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.
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,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0〉 1,it fluctuates around the endemic equilibrium of the deterministic model.
基金
National Natural Science Foundations of China(No.11071259,No.11371374)
Research Fund for the Doctoral Program of Higher Education of China(No.20110162110060)
