Stability analysis for a delayed SIRS epidemic model with vaccination and nonlinear incidence rate

摘要

In this paper, we have considered a delayed SIRS epidemic model with vaccination rate and nonlinear incidence rate. By analyzing the corresponding characteristic equations and based on Hurwitz principle, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed. It is proved that if the basic reproductive number (R)o＜1,the disease-free equilibrium is globally asymptotically stable by means of iteration method. The time delay has no effect on both global asymptotically properties of the disease-free equilibrium and local properties of the endemic equilibrium. Numerical simulations are carried out to testify the main results and suggest that the time delay may also have no effect on global asymptotically properties of the endemic equilibrium when the basic reproductive number (R)o＞1.On the other hand, we find it is difficult to prove the global asymptotically properties of the endemic equilibrium of the model if (R)o＞1,so we note the global asymptotically properties of the endemic equilibrium as an problem laid in this paper.