Global analysis of a general HBV infection model

Mathematical models have been used to understand the factors that govern infectious disease progression in viral infections. Two basic models of within-host viral infection, proposed by Nowak et. al. and Perelson et. al. respectively, have been widely used in the studies of HBV and HIV infections. However, the loss term of viral particles when it enters the target cells are both ignored by these two models. Leenheer and Smith provided a general virus dynamic model with the loss term of viral particles, which make the above two basic models only be special cases. But the basic reproduction numbers of all above models are proportional to the number of total cells of the host's organ prior to the infection(when used for HBV infection) or the normal target cell level(when used for HIV infection). On the other hand, the global asymptotically stable condition of the endemic equilibrium about Leenheer and Smith's model is related to the initial value of the growth function of uninfected cell. In this paper, we formulate an amended Leenheer and Smith's model with standard incidence, the basic reproduction numbers were no more dependent on the number of total cells of the host's organ. If the basic reproduction number of virus is less than one, the infection-free equilibrium is globally asymptotically stable and the virus is cleared; if the basic reproduction number is great than one, then the virus persist in the host, and solutions approach either an endemic equilibrium or a periodic orbit. The periodic orbit can be ruled out in some cases but not in general. The globally asymptotically stable condition of the endemic equilibrium is only determined by the model parameters.