The Analysis Of Hbv Models With Cytokine-mediated’Cure’ And Immune Impairment

In this paper. we constuct and analyze HBV infection models considering noncy-tolytic cure, immune response delay and immune impairment. First, we set up a four-dimensional HBV model, considering the dynamics of healthy cells, infected cells and immune response cells in body. Moreover, we consider an HBV model with immune response delay and an HBV model with antibody and CTL immune response. Then we analyze local and global stability of steady states, meanwhile we give the biological interpretation, There are four chapters in the following.In chapter one, we simply introduce the mechanism of Hepatitis B. the transmission theory and the measure of the vaccinate and treatment. We also give the related theorems about epidemic dynamics, virus dynamics and the stability theory of ordinary differential equation and basic knowledge.In the second chapter, we consider an HBV model with immune impairment and cytokine-mediated’cure’. We study the local and global stability, it is obtained that if the infection-free and immune-free equilibrium are locally stable, they are certainly glob-ally stable. We can also see that the system is permanent whenever infection equilibrium exists.In the third chapter. we consider an HBV model with immune response delay. By studying the model, we get that the delay have no effect in the local and global stability of the infection-free and immune-free equilibrium. However. it have influence in the infection equilibrium. In the fourth chapter, we give a four-dimensional HBV model with antibody and CTL immune response. We study the local stabilities of the equilibria, and analyze the impact of immune impairment to HBV infection.In the fifth chapter, we give the Summary and discussion.Finally, this article gives a reasonable strategy about how to control and cure of HBV. thus provides some suggestions on how to prevent and cure of HBV.