Predator-Prey Mathematical Model With Both The Populations Affected By Diseases

In this paper,based on the background of ecological epidemiological,we estab-lish two predator-prey mathematical models with both the populations affected by diseases,and analyze their behavior.In the first chapter,we introduce the research background and progress of the study of some predator-prey models and some basic theory.In the second chapter,we construct a dynamic model considering bilinear func-tion.Firstly,we show non-negativity and boundness of the solution of the system.Secondly,we analyze the existence of equilibrium point.Then,we prove local asymp-totic stability of equilibria.Finally,we obtain the globally asymptotic stability of equilibria.In the third chapter,we establish a dynamic model considering Holling type II functional response function.Firstly,we prove the non-negativity and boundness of the model solution,and then discuss the existence of equilibrium point.Secondly,we show local asymptotic stability of equilibria.Finally,we obtain the globally asymptotic stability of equilibria.In the last chapter,we make a brief review of the above conclusion,and present the biological meaning for these models.And we analyze some shortcomings of this thesis and point out some questions and future work.