Theoretical assessment of avian influenza vaccine

Folashade B. Agusto, Abba B. Gumel

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


This study presents a deterministic model for theoretically assessing the potential impact of an imperfect avian influenza vaccine (for domestic birds) in two avian populations on the transmission dynamics of avian influenza in the domestic and wild birds population. The model is analyzed to gain insights into the qualitative features of its associated equilibria. This allows the determination of important epidemiological thresholds such as the basic reproduction number and a measure for vaccine impact. A sub-model without vaccination is first considered, where it is shown that it has a globallyasymptotically stable disease-free equilibrium whenever a certain reproduction threshold is less than unity. Unlike the sub-model without vaccination, the model with vaccination undergoes backward bifurcation, a phenomenon associated with the co-existence of multiple stable equilibria. In other words, for the model with vaccination, the classical epidemiological requirement of having the associated reproduction number less than unity does not guarantee disease elimination in the model. It is shown that the possibility of backward bifurcation occurring decreases with increasing vaccination rate (for susceptible domestic birds). Further, the study shows that the vaccine impact (in reducing disease burden) is dependent on the sign of a certain threshold quantity (denoted by ∇p). The vaccine will have positive or no impact if ∇p is less than or equal to unity. Numerical simulations suggest that the prospect of effectively controlling the disease in the avian population increases with increasing vaccine efficacy and coverage.

Original languageEnglish (US)
Pages (from-to)1-25
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
StatePublished - Jan 2010
Externally publishedYes


  • Avian influenza
  • Backward bifurcation
  • Equilibria
  • Reproduction number
  • Stability
  • Vaccine efficacy
  • Vaccine impact

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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