Qualitative Analysis Of A Diffusive Predator-prey Model With Disease And Holling Ⅱ Functional Response

In this paper, a diffusive predator-prey system with disease and Hollingâ…¡functional response is in-vestigated. The full text is divided into seven sections.First, the background is outlined. Second, the local asymptotic stability of the non-negative equilibria is obtained by local linearization analysis.In section 3, a prior upper and lower bounds for positive steady states is given.In section 4, it has been proved that the non-negative equilibria is global asymptotically stable by constructing some suitable Lyapunov function. In section 5 and 6, we study the non-existence and existence of non-constant positive solution.The methods are based on Leray-Schauder degree theorem. In section 7, it has been proposed that there are still some problems in the system of the paper we can study.