Dynamics of a delay differential equation model of hepatitis B virus infection

Stephen A. Gourley, Yang Kuang, John D. Nagy

Research output: Contribution to journalArticlepeer-review

158 Scopus citations


We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.

Original languageEnglish (US)
Pages (from-to)140-153
Number of pages14
JournalJournal of biological dynamics
Issue number2
StatePublished - Apr 2008


  • Basic infection reproduction number
  • Global stability
  • Mass action
  • Standard incidence
  • Time delay

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology


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