Speaker: Sarah Hews
Department of Mathematics and Statistics
Arizona State University

Title: Rich dynamics of an HBV model with logistic hepatocyte growth

Abstract: Chronic hepatitis B (HBV) infection is a major cause of human suffering, and a number of mathematical models have examined within-host dynamics of the disease. Most previous HBV infection models have assumed that (a): hepatocytes regenerate at a constant rate from a source outside the liver and/or (b): the infection takes place via a mass action process. Assumption (a) contradicts experimental data showing that healthy hepatocytes proliferate at a rate that depends on current liver size relative to equilibrium mass while assumption (b) produces problematic basic infection number. Here we replace the constant infusion of healthy hepatocytes with a logistic growth term and the mass action incidence by standard incidence; these modi cations enrich the dynamics of a well-studied model of HBV pathogenesis. In particular, in addition to disease free and endemic steady states, the system also allows a stable periodic orbit and a steady state at the origin. Since the system is not differentiable at the origin, we use a ratio-dependent transformation to show that there is a region in parameter space where the origin is stable. When the viral basic reproductive number, R0, is less than 1, the disease free steady state is stable. When R0 > 1 the system can either converge to the chronic steady state, experience sustained oscillations, or approach the origin. We characterize parameter regions for all three situations and show how they depend on the basic reproductive number and the intrinsic growth rate of hepatocytes.