Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth.
Chronic hepatitis B virus (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 some equilibrium mass, while assumption (b) produces a problematic basic reproduction number. Here we replace the constant infusion of healthy hepatocytes with a logistic growth term and the mass action infection term by a standard incidence function; these modifications 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 globally stable. When the basic reproduction number, R (0), is less than 1, the disease free steady state is stable. When R (0) > 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, identify a Hopf and a homoclinic bifurcation point, and show how they depend on the basic reproduction number and the intrinsic growth rate of hepatocytes.
Hews
Sarah
S
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, USA. sarah.hews@asu.edu
Eikenberry
Steffen
S
Nagy
John D
JD
Kuang
Yang
Y
D050936:Basic Reproduction Number; D006515:Hepatitis B virus / Q000276:immunology*; D019694:Hepatitis B, Chronic / Q000453:epidemiology / Q000276:immunology* / Q000821:virology; D022781:Hepatocytes / Q000276:immunology / Q000821:virology; D006801:Humans; D018448:Models, Immunological