Global Analysis Of Two Kinds Of Epidemic Dynamics Models

This paper mainly studies the dynamic properties of two kinds of epidemic models.One is the single population epidemic model,and the other is the eco-epidemic model with two populations.This thesis is composed of six chapters.In chapter one,we mainly introduce the research background,significance,research status and development trend of the epidemic models,we also summarize the research contents of this thesis.In chapter two,we mainly give the relevant preliminary knowledge and the theory of stability about the epidemic dynamic models.In chapter three,a class of SEIR epidemic model with nonlinear incidence rate is studied,and the threshold which determines whether the disease is epidemic or not is given,the local and global stability of the two kinds of equilibrium points are obtained.In chapter four,we investigate the dynamics of an SEIRS epidemic model with media coverage.For three special situations,by the Routh-Hurwitz criteria and geometric approach,the local and global stability of the positive equilibrium is analyzed,and the conditions for the existence of Hopf bifurcation at the positive equilibrium are given.In chapter five,the global behavior of a predator-prey epidemic model with disease in the prey is studied.Based on the Routh-Hurwitz criteria,Liapunov function and LaSalle invariant set principle,local and global stability of the disease-free equilibrium,boundary equilibria and positive equilibrium are derived.The existence of Hopf bifurcation at the positive equilibrium is proved by numerical simulations.In chapter six,we summarize the main research results of the two kinds of dynamics models,some relevant issues need to be further studied are also presented.