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

Abstract

In this paper, the authors first show that if R0 ≤ 1, the infection free steady state is globally attractive by using approaches different from those given by Min, et al.(2008). Then the authors prove that if R0 > 1, the endemic steady state is also globally attractive. Finally, based on a patient's clinical HBV DNA data of anti-HBV infection with drug lamivudine, the authors establish an ABVIM. The numerical simulations of the ABVIM are good in agreement with the clinical data.

Discrete virus infection model of hepatitis B virus

“…Based on previous researches [6,7], this study proposes a discrete difference equation model to describe virus infection dynamics. Theorem 3.2 in this paper gives the condition that the virus free equilibrium point of our model is locally stable.…”

“…(1) needs to be modified. In previous research [6,7,15], aiming at this irrationality, the authors use the standard incidence rate instead of the simple occurrence rate, and propose a modified model:…”

“…Based on the differential equation virus infection given in [6,7], this study proposes the following assumptions.…”

“…In a series of previous researches on modeling virus infection dynamics, there exist two different kinds of mathematical models: the differential description of continuous time models [2][3][4][5][6][7] and the difference description of discrete time models [8][9][10][11].…”

“…In previous researches [6,7,[12][13][14][15], the mechanisms of virus infections have been described via differential equation models. Based on an HBV-infected patient's clinical data [2] with cell division mechanism, this study proposes a discrete HBV infection model, analyzes the stability of the disease free equilibrium, models and simulates the dynamics of the HBV-infected patient's anti-HBV infection treatment [2].…”