Stability Of An SIR Epidemic Model Dynamics

In this paper we mainly discuss the stability of epidemic system, it’s organized as follows:Introduction introduces some background information and results of this paper in sec-tion1. The dynamics of the follow delayed epidemic model with non-monotonic incidence rate is considered in section2, By Lyapunov functional techniques and some linear systems, we show that the disease-free equilibrium and endemic equilibrium are globally asymptotically stable. This conclusion extends the result of the reference[Commun Nonlinear Sci Numer Simulat15(2010)459-468]. An SIRS epidemic model with vertical transmission and pulse vaccination and non-monotonic incidence rate is investigated in section3, the model takes the following form Firstly, by Floquet theorem, impulsive comparison theorem and iteration method, we can establish that (2) with Ro<1and6(1-p)-γ<0is global asymptotic stability of the disease-free equilibrium. Secondly, we derive sufficient conditions for the permanence of this system. The model (2) is the model of the reference[Nonlinear Analysis:Hybrid Systems8(2013)13-21]. when p=1. This conclusion extends the result of Zhang H.ect.