The Study On Some Eco-epidemiological Models For Predator With Epidemic

In this paper, by use of the theory on impulsive differential equa-tion,we study some eco-epidemiological models for predator with epidemic.There are four chapters.The preface is in chapter 1, we introduce some knowledge of eco-epidemiological models and some prelimineries.In Chapter 2, we formulate and analyze the predator-prey model of predator with epidemic. The boundness of solution and the sufficient condi-tion of locally asymptotically stable of the equilibrias are studied,futhermore, the globle stability of all the equilibrias,and the sufficient condition of predator-extincting and disease persistence are also obtained.In Chapter 3, the SIRS epidemic model with nonlinear contact rate and pulse vaccination are discussed. Sufficient conditions for global asymp-totic stability of the infection-free periodic and uniform persistence of this model are obtained.In Chapter 4, we consider a stage-structured predator-prey model of predator with time delay and impulsive transmitting on predators. Suffi-cient conditions which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactic basis for the practical pest management.