The Research Of HBV Infection Dynamics

In this paper, the stability and periodicity of the hepatitis B virus infection dynamic systems were studied. The sufficient conditions of stability and existence of the positive periodic solution were obtained. The full text is composed of three parts as follows.In the first chapter, the history of virus infection dynamic's development, the existed related works and the origin of the problem were discussed.In the second chapter, firstly, a new hepatitis B virus infection dynamic in immune response was established. By using Routh-Hurwitz criteria, the sufficient condition of local asymptotical stability of a positive equilibrium point was obtained. Secondly, the mathematical model with delay in immune response was discussed, and it was found that the stable switch will occur with the delay increasing. Finally, the mathematical model with three different delays was established, the sufficient condition of local asymptotical stability of a immune-exhausted equilibrium point was obtained.In the third chapter, by reason of the infected cells can also breed as the uninfected cells, and considering the effect of periodically changing environment, a chronic hepatitis B virus infection periodic model was established, in which the birth rate of infected cells equals to that of uninfected cell. Based on the theory of coincidence degree, the existence condition of positive periodic solution of the model was established. It can explain why the pathogens in blood exist wave phenomenon in patients with chronic HBV infection.