Analysis Of Epidemic Models For A Few Kinds Of Vector-borne Plant Disease

In this paper, we mainly study epidemic modlc of vector-borne disease,the dynamicl be-havior of the systems arc analyed.The article is divided into three chapters.The first chapter, introduction, we introduced the research background and some prereq-uisites.The second chapter, we research biological control strategy of vector-borne plant disease. In this chapter, we expand general model about the biological control plant disease, and consider transovarial transmission of virus and secondary infection between plants on the basis of the original model. We obtain the new basic reproduction number of virus, invasion threshold value of virus and invasion threshold value of parasitoid. At the same time giving a condition about the existence of periodic solution when pulse input parasitoid.In the third chapter, we propose an epidemic model with nonlinear incidences of a vector-borne plant disease to investigate the effect of insect vector on the dynamics of the plant disease. Firstly, we get the basic reproduction number R by the next generation matrix method. Sec-ondly, we get the expression of two equilibria:disease-free equilibrium and endemic equilibrium. Thirdly, by use of Lyapunov function and theory of additive compound matrix, we find that the basic reproduction number Ro is a critical threshold. If Ro≤1, then the discasc-free equilibrium is globally asymptotically stable, which means that the plant disease will die out eventually. If Ro>1, then the endemic equilibrium is globally asymptotically stable, which means that the plant disease will persist for all time.