Mathematical analysis of a basic virus infection model with application to HBV infection

Abstract

The basic virus infection model (BVIM) is widely used in the studies of hepatitis B virus (HBV) infection dynamics. This model assumes that the infection process follows a mass action law. The basic infection reproductive number of the model is proportional to the number of all cells of the host's organa prior to the infection. This suggests that the BVIM may not be a reasonable model for describing the HBV virus infection since it implies that an individual with a smaller liver may be more resistent to virus infections than an individual with a larger one. In this paper, we formulate a standard incidence based model that amends the BVIM (we shall call it ABVIM below) which will correct this mass action induced model artifact. If its basic infection reproductive number is less than 1, then every positive solution will converge to the infection-free steady state. We also present an application of ABVIM to some clinic HBV infection data. Copyright © 2008 Rocky Mountain Mathematics Consortium.