Stability Of Several Host-vector Epidemic Models

In this paper, the stability of several kinds of host-vector epidemic models are analyzed.The reproduction number R0 is obtained. And the existence and stability of the equilibrium are discussed. The numerical simulation are given to validate the conclusion.In this paper, the stability of host-vector epidemic models are analyzed. These estab-lished models consider these factors such as logistic growth, variable immunity, vaccination,the latent period, disease control, genetically modified mosquitoes. Broaden the research category of the model. These established models provides the theoretical basis of the control of host-vector epidemic.In chapter one, we mainly introduce the background, current situation, some corre-sponding main definitions and theorems about host-vector epidemic model.In chapter two, a host-vector epidemic model with logistic growth vector and variable immunity is formulated, vaccination and insecticides is used to control disease epidemic.The reproduction number is found by the next generation matrix method. The sufficient condition for the existence and stability of equilibria are obtained.In chapter three, we mainly study a SEIRSvIv vector-borne epidemic model with vaccination. The reproduction number R0 is found. This chapter is mainly through the stability theory, Lasalle invariant set theory, the second additive compound matrix theory for the existence and stability of equilibria.In chapter four, research the effects of RIDL on malaria control. The malaria infec-tion model is formulated. In considering the mosquito model without infection, malaria model in natural environment, malaria model with the released male mosquitoes carrying dominant lethal gene. The releasing of male mosquitoes carrying dominant lethal gene is very helpful to control disease.