Global Properties Of One Kind Of HIV Models

In recent years, the dynamics of infectious diseases has become a very im-portant part in mathematics and medical science, it has attracted more and more attentionfrom Mathematics educators and medical researchers. Especially, HIV infection model theoryhas a great value in both theory and application. One of the most important questions is toprove the infected steady state is globally asymptotically stable and to construct Lyapunovfunctions, which has received a great deal of attention of many mathematicians and biologists.Base on the existed HIV infected models. We make much investigation in the three models,we also consider to improve and popularize the two models.This paper is composed of six chapters.In the first chapter, we introduce the HIV virus and the specific methods of studyingthe dynamics of infectious diseases. In addition, the main work of this paper is also simplyintroduced in this chapter.In the second chapter, we introduce the knowledge which need to use in this article andvarious forms of Lyapunov fouctions.In the third chapter, we will introduce and investigate the simplest HIV model. Byconstructing the appropriate Lyapunov functions, we prove the positive equilibrium of themodel is globally asymptotically stable, then we improve and popularize the model. By usingthe Lyapunov functions and the theory of stability, we obtain the general result.In the fourth chapter, we introduce and investigate the second model and prove thepositive equilibrium of the second model is globally asymptotically stable, then we improve and popularize the model. By using the Lyapunov functions and the theory of stability, weobtain the general result.In the fifth chapter, we introduce and investigate the third model and prove the positiveequilibrium of the third model is globally asymptotically stable.In the last chapter, some concluding remarks for the future work are given.