Global Dynamics Of HBV Model With Immune Response

In this paper, we investigate the dynamical behavior of HBV infection models with CTL immune response. First, we set up an HBV model about the populations of uninfected cells, infected cells that produce virus and CTL immune cells in body after a person was infected by HBV. Moreover, we consider an HBV model with time delay and CTL immune, and study the effect of time delay on stability of the equilibria of the system. 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 research progress of HBV dynamic model within the host and related work of this paper.In the second chapter, we study a mathematical model of HBV infection to describe two types of CTL immune response, which are lytic and nonlytic components. It is shown that if the basic reproduction number is less than one, the disease-free steady state is globally asymptoti-cally stable, and it is greater than one, the trivial equilibrium loses stability and the disease is persistent. Furthermore, using a geometrical approach, we obtain a sufficient condition for the global stability of the disease steady state.In the last chapter, an HBV model with time delay and CTL immune is proposed based on some important biological meanings. We get globally stability of the disease-free equilibrium and uniform persistence of the system. And the existence of Hopf bifurcation of the infected equilibrium is analyzed. The effect of time delay of CTL on the stabilities of the positive equi-librium is studied. From this article, the effect of CTL immune response during HBV infection process in mathematics is further studied. It gives us a better understanding of disease development and provides some suggestions on how to prevent and cure of HBV.