The Resecarch Of Eco-epidemiological Models Incorporating Prey Refuges

As infectious diseases can be recognized as one of the major tools in regulating and controlling the size of human population and animal population, disease in ecological systems is an important issue.Most of studies about eco-epidemiological system mainly focused on parasite infection in prey population only. The main aim of this topic is to eradicate the disease transmission in the systemFirstly, we considere the eco-epidemiological model with prey refuges incorpo-rating Holling Ⅰ, Holling Ⅱ, Holling Ⅲ, Holling type and general functional response, we assume that predators prey upon both susceptible and infectious prey. In chap-ter three, we apply LaSalle invariable set, limit theory, Dulac rule and Liapunov function to investigate five eco-epidemiological models with the bilinear incidence rate and prey refuge incorporating Holling Ⅰ, Holling Ⅱ, Holling Ⅲ, Holling type and general functional response, respectively. We study the local and global stability of the initial equilibrium point, predator and disease free equilibrium point, predator-free equilibrium point, disease-free equilibrium point, and then the permanence of the considered model.Secondly, the saturation incidence rate are more reasonable than the bilinear in-cidence g(I)S=βIS since it included the crowding effect and behavior changes,and it can prevent the unbounded of the contact rate. Motivated by this, in chapter four, we considere eco-epidemiological models with the saturation incidence rate and the five Holling type response functions, respectively. We focus on local and global sta-bility of the initial equilibrium point, predator and disease free equilibrium point, predator-free equilibrium point, disease-free equilibrium point, and investigate the permanence of the constructed models according to the method of the average Lia-punov function. The aim of research on the eco-epidemiological model is to prevent the spread of the infectious disease. Therefore, we obtain the sufficient conditions which make the disease-free equilibrium point stable or unstable.