| The epidemic model with vaccination and re-infection is formulated and analyized. It is assumed that the sussceptible individuals arc infected after being vaccinated. The explicit expression of the basic reproduction number R0 is obtained. The model is shown that the unique disease free equlibrium is globally asymo-totically when R0<1. It is also proved that there exists an unique endemic equilibrium if R0> 1.The stability of disease free equlibrium and endemic equilibrium is discussed by the theory of Lyapunov function,Routh-Hurwitz criterion and second additive Matrix. |
