Stability And Bifurcation Of Eco-epidemiological Dynamics Model

Qualitative analysis of eco-epidemiological models has become a very important part in biological mathematic,it plays an important role in controlling disease spread and the impact of disease on population size.In this thesis,based on K-monotone theory,LaSalle invariant set principle,geometric mothed of global stability and bifurcation theory,we disussed the dynamic behavior of the eco-epidemiological model with vertical transmission in diseased prey and eco-epidemiological model with latent effect in competing populations,mainly including the existence and stability of equilibrium point,persistence and Hopf bifurcation were studied.This paper is composed of six chapters.In first chapter,we introduce the signification of eco-epidemiology model exploration and its research status.In second chapter,we introduce some basic concepts and methods of this paper.In third chapter,Based on K monotone theory of Simth,sufficient conditions are given to ensure the global stability of the positive equilibrium for a class of kolmgorov system by constructing the associate systems.By virtue of these results,we investigate the global stability of Lotka-Volterra systems and two-dimensional kolmgorov pery-predator system.In fourth chapter,we establish an eco-epidemiological model with vertical transmission in diseased prey.The boundedness of solutions and the existence of non-negative equilibrium points are discussed,by applying Hurwitz criterion and Li-Muldoweny geometric criterion to analyze the stability of the model,the sufficient conditions for local asymptotic stability of equilibrium points and global asymptotic stability of endemic equilibrium points are obtained.In addition,.we study the persistence of the system and the sufficient conditions for the existence of Hopf bifurcation is obtained.In fifth chapter,by introducing the latent effect of disease,we consider an eco-epidemiological model in competitive populations,and study the stability of the model by using the limit system theory and LaSalle invariant set principle.The Driessche-Zeeman conjecture and Gyllenberg-Liu-Yan conjecture are solved completely and partially based on the geometric method of global stability based on time-averaged property.In sixth Chapter,we summarizethe main results of the eco-epidemiological model in this paper,and prospect for further work.