Analysis Of Epidemic Models For A Few Kinds Of Plant Disease

In this paper, according to the work of some scholars in recent years, we study epidemicmodles of soil-borne plant disease and vector-borne plant disease, the dynamical behavior of thesystems are analyed. The article is divided into three chapters.In Chapter 1, some background and prelimineries are introduced.In Chapter 2, biological control for soil-borne plant disease are studied. We extend amodel for biological control of soil-borne plant pathogens, which is a compartmental model ofthe interaction between plant host, soil- borne pathogen and microbial antagonist, concerningreleasing antagonist (the constant input or the impulse input). We get the sufcient conditionsfor the existence and stability of the equilibria of the system. We prove that there is a locallyasymptotic stable periodic solution of pathogen-extinction. Qualitative analysis of the modelshowed that the amounts of biological control agent is the important factors in determining thefinal outcome of the system. It is concluded that the approach of releasing antagonist providesreliable tactic basis for efective biological control. Numerical simulation are also performed.Finally, a brief discussion is provided in the last section.In Chapter 3, we analyse an epidemic model with vector-borne plant disease. We considervertical transmission in the vector population and the recovered plants which get infected byinfected vector, and study the efects that they have on the dynamics of the disease. The modelshows that the dynamics is completely determined by the basic reproduction number R0. IfR0≤1, the disease-free equilibrium is globally stable and the disease dies out. If R0> 1, thedisease persists, a unique endemic equilibrium exists and is globally asymptotically stable. Aqualitative analysis as well as some numerical examples are given for the model.