A Prey To Consider A Constant Input Of The Ecology Of Infectious Diseases

In traditional epidemiological model, we generally consider the susceptibles, the infec-tives, the removed. Talking into account the relations between the two populations of the ecosystem such as the relation between the prey and the predator, we mainly research three models with the disease in the prey in the follows.In chapter 2, a ratio-dependent predator - prey system with disease in the prey is formulated and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions are analyzed. And we study nature of equilibria by Hurwitz criterion and the second compound matrix.In chapter 3, we analyze and formulate the eco-epidemiological model with the disease in the prey, considering the prey population with the constant of recruitment. And we study the boundedness of solutions and the existence of the equilibrias, obtain the conditions of locally asymptotically stable of the equilibrias, analyze the global stability of the equilibrias by constructing appropriate Lyapunov functions.In chapter 4, we analyze and formulate the eco-epidemiological model with impulsive birth. Using the discrete dynamical system determined by stroboscopic map, we obtain the exact cycle of system in the absence of the infection. And we proved the local stability of the period infection-free solution by applying the Floquet theory and impulsive differential inequality. Finally, we give numerical simulation of the result.