An Eco-epidemiological Model With Cooperative Behavior And Predator Disease

In this thesis,a predator-prey model with diseased predator is studied.Considering the cooperative predator behavior of predator population,the influence of epidemic and population behavior on the survival of predator population is studied by analyzing the dynamic properties of the eco-epidemic model.In the first chapter,the research background of ecological model and epidemic model is introduced in detail,and the development history of ecological epidemic model is elaborated.Finally,the mathematical work and theoretical knowledge needed in this paper are briefly explained.In chapter 2,a predator-prey model with cooperative behavior and predator s illness is established.The non-negativity and boundedness of the solution of the system are proved by using ordinary differential knowledge and counter-evidence method.Secondly,the dynamic properties of the disease-free sub-model are discussed,and the global stability of the boundary equilibrium is proved by constructing appropriate Lyapunov function.The predator-prey coexistence is discussed by using Dulac function.The global stability of the equilibrium point is discussed.The existence of the Bogdanov-Takens bifurcation and the conditions for generating Hopf bifurcation are also discussed.Thirdly,the dynamic properties of the whole model are discussed.The local stability conditions of the positive equilibrium point of the system are given by using the Routh-Hurwitz criterion,and the bifurcation of the system with disease infectivity as the bifurcation parameter is discussed.Finally,the numerical simulation is carried out by using Mat lab software to verify the theoretical results.The third chapter summarizes the maiu work of this thesis,and gives the problems and significance worthy of further study.