Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth

Sarah Hews, Steffen Eikenberry, John D. Nagy, Yang Kuang

Research output: Contribution to journalArticlepeer-review

81 Scopus citations


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, 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, 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.

Original languageEnglish (US)
Pages (from-to)573-590
Number of pages18
JournalJournal Of Mathematical Biology
Issue number4
StatePublished - Jan 1 2010


  • HBV
  • Homoclinic bifurcation
  • Hopf bifurcation
  • Logistic hepatocyte growth
  • Origin stability
  • Ratio-dependent transformation

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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