Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains

F. B. Agusto, A. B. Gumel

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

A new deterministic model for the transmission dynamics of the lowly- and highly-pathogenic avian influenza (LPAI and HPAI) strains is designed and rigorously analyzed. The model exhibits the phenomenon of backward bifurcation, where a stable disease-free equilibrium co-exists with a stable endemic equilibrium whenever the associated reproduction number is less than unity. It is shown that the re-infection of birds infected with the LPAI strain causes the backward bifurcation phenomenon. In the absence of such re-infection, the disease-free equilibrium of the model is globally-asymptotically stable when the associated reproduction number is less than unity. Using non-linear Lyapunov functions of Goh-Volterra type, the LPAI-only and HPAI-only boundary equilibria of the model are shown to be globally-asymptotically stable when they exist. A special case of the model is shown to have a continuum of co-existence equilibria whenever the associated reproduction numbers of the two strains are equal and exceed unity. Furthermore, numerical simulations of the model suggest that co-existence or competitive exclusion of the two strains can occur when the respective reproduction numbers of the two strains exceed unity.

Original languageEnglish (US)
Pages (from-to)147-162
Number of pages16
JournalMathematical Biosciences
Volume243
Issue number2
DOIs
StatePublished - Jun 1 2013
Externally publishedYes

Keywords

  • Avian influenza
  • Co-existence
  • Competitive exclusion
  • Highly-pathogenic
  • Lowly-pathogenic

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains'. Together they form a unique fingerprint.

  • Cite this