A Class Of Stochastic Model Of HIV Affected By The Media

Stochastic differential equations, an interdisciplinary subject developed in the middle of twentieth Century, is a new branch of mathematics,established in ordinary differential equation, dynamic system and stochastic analysis. Its application is very extensive. Based on the theory of stochastic differential equations, according to the influence of media on the HIV, this paper established a stochastic model of HIV. It has proved the existence and uniqueness of the solutions and discussed the asymptotic behavior of solutions etc.This article is divided into three chapters.The first and the second chapter are the preface and the preliminary knowledge respectively, the third one is stochastic model of HIV with the influence of media.Firstly, we prove the existence and uniqueness of the solutions and discuss the asymptotic behavior of solutions, from which we get the conclusion that the system is globally asymptotically stable on the condition of R<1, which implies that infected population will be extinct.Furthermore, we discuss the stability of free equilibrium and obtain the almost sure exponential stability conditions.Then, to prove the correctness of the theorem, numerical simulation is presented.At last, we make a simple but comprehensive summary to the full text and speculate on the stochastic model of HIV.