Global dynamics of a two-strain avian influenza model

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46 Scopus citations

Abstract

A deterministic model for the transmission dynamics of avian influenza in birds (wild and domestic) and humans is developed. The model, which allows for the transmission of an avian strain and its mutant (assumed to be transmissible between humans), as well as the isolation of individuals with symptoms of any of the two strains, has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiological threshold, known as the reproduction number, is less than unity. Further, the model has a unique endemic equilibrium whenever this threshold quantity exceeds unity. It is shown, using a non-linear Lyapunov function and LaSalle invariance principle, that this endemic equilibrium is globally asymptotically stable for a special case of the avian-only system. Numerical simulations show that, on average, the isolation of individuals with the avian strain is more beneficial than isolating those with the mutant strain. Furthermore, disease burden increases with increasing mutation rate of the avian strain.

Original languageEnglish (US)
Pages (from-to)85-108
Number of pages24
JournalInternational Journal of Computer Mathematics
Volume86
Issue number1
DOIs
StatePublished - Jan 1 2009

Keywords

  • Avian influenza
  • Equilibria
  • Lyapunov function
  • Reproduction number
  • Stability

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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