The Global Stability Of Several Types Of Vector Infectious Disease Models

Firstly, we formulate an epidemic model with vaccination and re-infection. We rede?ne the basic reproduction number R0. It is shown that the disease-free equilibrium is globally stable for R0? 1. The endemic equilibrium of this model is globally stable for R0> 1, the disease will be permanent and bring on the epidemic.Secondly, we formulate a vector-borne epidemic model with saturated incidence rate.If R0? 1, the disease-free equilibrium of the model is globally stable, and the disease is gradually dying. The positive equilibrium is globally asymptotically stable for R0> 1, the disease will be permanent and bring on.Finally, a vector-borne epidemic model with horizontal transmission is formulated.Global stability of disease-free equilibrium is proved if R0< 1.It is proved that disease-free equilibrium is global stability which use further application of Lyapunov function and LaSalle invariance principle. When R0> 1, the system has a unique positive equilibrium point, and a second additive theory is used to prove that the positive equilibrium is globally stable.