The Study Of Influence Of Environment And Transmission Route For Some Classes Of Epidemic Models

In this paper some mathematical models are investicaled.(1) A mathematical model for coupling within-host and between-host;(2) the effect of transmission route on plant virus epi-demic development and disease control. We discuss the dynamic behaviours of the models.The article include three chapters.In chapter1, we introduce the research background of this article, the main task and some important preliminaries.In Chapter2,we discuss a mathematical model for coupling within-host and between-host.In the first section, we analyze a mathematical model with nonlinear incidence rate which in an environmentally-driven infectious disease. We define a new reproductive number Rvo for the fast systems,it is easy to show that infection-free equilibrium Uo is locally asymptotically stable if Rvo<1;When Rvo>1,using the Routh-Hurwitz stability criterion we obtain the local stability of U(E),under the condition that the fast system has the stable interior equilibrium U(E),we dynamic linkage for the fast-and slow systems is through the environmental contamination variable E, we obtain the condition that the existence and stability of an interior equilibrium of the full system. At last,a numerical analysis is given to show the effectiveness of the main results.In the second section,an environmentally-driven infectious disease model with a standard incidence rate is studied.We get the sufficient conditions for the existence and stability of the equilibria of the full system.A numerical analysis is given to show the effectiveness of the main results.In Chapter3,we analyze the effect of transmission route on plant virus epidemic devel-opment and disease control. By construction a suitable Lyapunov functional,the infection-free equilibrium Uo is globally asymptotically stable if Ro≤1;The endemic equilibrium exists if Ro>1. We analyse the model to determine the effect of direct transmission on plant disease control directed against indirect transmission. In the end, numerical simulations are carried out to explain the mathematical conclusions.