The Study Of Two Types Of Vector-borne Disease Models

In this paper, we mainly study two types of vector-borne disease models and a class of eco-epidemic model with disease in the prey. By using the relevant theories of math,we discuss someof the dynamic behaviors of the models and obtain some useful results, which are of considerablesignificance in theory and application.This article includes three chapters.Chapter 1 is a preface, which introduces the research background and the main works aswell as some preliminaries of this paper.In Chapter 2, we formulate two types of vector-borne disease models. In the first sec-tion, the article discussed a dynamical model considering vector-borne and viruses mutate. Byusing the next generation method, the threshold parameter is obtained which determines thedisease outbreak or not. In special case, a Lyapunov function is constructed and using LaSalletheory and Routh-Huruitz criterion, we study the local and global asymptotic behavior of thedisease-free equilibrium and boundary equilibrium.Finally, it is shown that the unique coexis-tence equilibrium is local asymptotically stable by using a krasnoselskii sub-linearity trick. Inthe second section, the article discussed a dynamical model for tularaemia considering two vec-tors. Obtain a basic reproductive number which determines the disease outbreak or not and thesufcient condition of global asymptotic stability of the disease-free equilibrium. Furthermore,we establish a dynamical model considering several vectors for tularaemia.In Chapter 3, we study a eco-epidemic model with predator-dependent consumption Hassell-Varley functional response for the predator and stage structure and disease in the prey. We provethat all solutions of the model are uniformly ultimately bounded, by using comparison theoremof impulsive diferential equation and some theories of the delay diferential equation,we obtainthe conditions for the global attractivity of the susceptible pest-eradication periodic solutionand the permanence of the system.