Analysis Of Two Kinds Of Viral Infection Model

AIDS has became the main disease that threats to human health. China has reported its first AIDS case since 1985.After that the number of people who infected with AIDS virus(HIV) sharply increased. So the research on AIDS treatment is a very urgent task. Many scholars on HIV treatment has done a series of research, and has made fruitful results. It’s very meaningful for the treatment and control of this disease to do a research on infection process of AIDS virus by modeling a mathematical model and puts forward a scientific and reasonable treatment plan.In recent years research of HIV infection dynamics basically is based on Perelson’s standard HIV infection model.They considered more other factors to modify the standard HIV infection model. Some of them research results concentrated in investigation drug treatment on effects of HIV infection process, Some of them also concentrated in research human itself immune capacity on HIV infection process of effects. However both factors are considered is rarely. So in this paper, we first consider the HIV infection model with delayed immune reaction, while the nonlytic immune reaction is also considered into our model. By analysis our HIV infection model, we obtain the necessary conditions for the existence of the infection-free equilibrium, the infected equilibrium without immunity and the infected equilibrium; with Routh-Hurwitz discriminant guidelines, we get that the infection free equilibrium 0E is globally asymptotically stable when 0R ?1, and the infected equilibrium without immunity 1E is local asymptotically. Under the condition 0R ?1 ?b?/ cd, we obtain the sufficient conditions to the local stability of the infected equilibrium with immunity 2E; By constructing a Lyapunov functional, we do a research on global stability of the equilibrium point; with the relevant conclusions of the eigenvalue distribution of transcendental equation, we get the the conditions that Hopf branching occur, By applying normal form theory and center manifold theorem, the direction of Hopf bifurcation and stability of bifurcating periodic solutions have been investigated.Secondly, we consider that a person infected HIV virus will accept drug treatment, while the body’s own immune function also plays an important role. Generally, the drug-taken time of AIDS is periodic, so the drug effect on HIV can be considered as periodicity. Besides, studies have shown that the body’s immune system also presents a certain periodicity. Based on the above factors we establish a HIV model with periodic immune response and periodic medication, and analyse the non-negative and boundedness of this model. Using the theory of periodic coefficient system, we analyse the global stability of disease-free equilibrium, the results show that the infection-free equilibrium is the global asymptotic stability when 0R ?1 and the system is uniformly bounded.Finally, in order to verify the correctness of the theory, we select appropriate parameters to make numerical simulation using MATLAB, the results show that our analysis is correct.