Dynamic Analysis And Research For Several HIV Pathological Models

This paper established three HIV infection mathematical models, the dynamicsof these models are analysed by the basic theory and method of differential equationsin mathematics. Finally, numerical simulations are consistent with the conclusionswhich we obtained in paper and these results has the better biological significance.This paper is consist of the following four chapters.In the first chapter, the background and significance of AIDS research is brieflyreviewed and some mathematical models of HIV infection are given. Furthermore, themain work in this paper are introduced simply, some relevant knowledge are given inthe end(definitions, theorems and lemma, etc).In the second chapter, we consider a pathological model for HIV with immunedelay. The global asymptotic stability of the infection-free equilibrium is analyzed byconstructing a Lyapunov function, and the sufficient conditions for the local stabilityof the other two infection equilibria are obtained. Then, the existence of Hopfbifurcation near the CTLs-present infection equilibrium is discussed. In the end, somerelated numerical simulations are illustrated on some conclusions of the CTLs-presentinfection equilibrium.In the third chapter, a better pathological mathematical model for HIV by bringinginto the two factors of saturating infection rate and time delay is established. We studythe global asymptotical stability of the viral free equilibrium of the model, and obtainthe sufficient conditions for the local asymptotical stability of the other two infectionequilibria. Finally, some related numerical simulations are also presented to supportour results.In the fourth chapter, we consider the dynamics of HIV infection model withHolling II Functional Response by bringing delay into the infection equation and virusproduction equation, respectively. The global asymptotic stability of the infection-free equilibrium is analyzed by characteristic equation and fluctuation lemma, and thesufficient condition for local stability of the infection equilibrium is obtained. In theend, some related numerical simulations are illustrated to verify our conclusions.