Global stability of endemic equilibrium point of basic virus infection model with application to HBV infection

The basic virus infection model (BVIM) is widely used in the studies of hepatitis B virus (HBV) infection dynamics. The basic infection reproductive number of the BVIM is proportional to the number of all cells of host’s organ prior to the infection. This suggests that the BVIM may not be a reasonable model for describing HBV virus infection since it implies that an individual with smaller liver maybe more resistent to virus infections than an individual with a larger one. In [1], we formulated a standard incidence based model that amended the BVIM (named ABVIM) which corrected this mass action induced model artifact. We have proved that if its basic infection reproductive number R0 < 1, then the infection free steady state is globally attractive. In this paper, we first show that if R0 ≤ 1, the infection free steady state is globally attractive by using approaches different from those given in [1]. Second we will prove that if R0 > 1, then the endemic steady state is also globally attractive. Finally based on a patient’s clinic HBV DNA data of anti-HBV infection with drug lamivudine, we establish an ABVIM. The numerical simulations of the ABVIM are good in agreement with the clinic data.