An SIR Epidemic Model

In this paper, we study SIR epidemic model. In chapter two, we discuss an SIR epidemic model vertical transmission.It has concluded the basic reproduction number R0 and proved the globally asymptotic stabilities of the endemic equilibrium and the disease free equilibrium.So, the conclusion is that the disease will disappear under the certain conditions. In chapter three, SIS epidemic model with vertical transmission and a varying total population size is proposed.Basing on the Dulac judgment,the basic reproduction number R0 and the stability of the disease free equilibrium are obtained for the model.