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

F. B. Agusto, Abba Gumel

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 2013
Externally publishedYes

Fingerprint

Influenza in Birds
Influenza
avian influenza
Reproduction number
Reproduction
Backward Bifurcation
Globally Asymptotically Stable
Coexistence
Infection
Exceed
Competitive Exclusion
Model
Endemic Equilibrium
competitive exclusion
Birds
Deterministic Model
Volterra
Nonlinear Function
infection
Lyapunov Function

Keywords

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

ASJC Scopus subject areas

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

Cite this

Qualitative dynamics of lowly- and highly-pathogenic avian influenza strains. / Agusto, F. B.; Gumel, Abba.

In: Mathematical Biosciences, Vol. 243, No. 2, 06.2013, p. 147-162.

Research output: Contribution to journalArticle

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