Study Of Dynamical Models About Stochastic HIV

In this paper,according to the infection process and the pathogenic mechanism of HIV virus in the host,we establish dynamics of a stochastic HIV model with Holling-? type saturation infection,as well as the bilinear stochastic HIV dynamical model of virus-to-cell infection and cell-to-cell infection.Besides,the dynamical properties and biological meanings of each model are discussed.In Chapter 1,we introduce the historical background,prevalence status,pathogenic mechanism and research status of AIDS.Meanwhile,the main work of this article and some basic theory are briefly stated.In Chapter 2,firstly,we study a stochastic model about HIV,in which Holling-? type saturation infection incidence rate.Then,by constructing Lyapunov function,Chebyshev's inequality and Borel-Cantelli lemma,we give the non-negative and bound-edness of the global positive solutions.Finally,by constructing Lyapunov function,we obtain the sufficient conditions of extinction and persistence for the stochastic HIV mod-el with Holling-II type saturation rate.In Chapter 3,first of all,we establish the bilinear stochastic HIV dynamical model of virus-to-cell infection and cell-to-cell infection.Secondly,by constructing Lyapunov function and Gronwall inequality,the existence and non-negative of stochastic solutions is proved.Finally,by constructing suitable Lyapunov functional and dividing area,we get the conditions for the extinction and the unique stationary distribution of the HIV dynamical model.In the last chapter,the main work of this paper is summarized,and the issues and significance worthy of further study are given.