Role of incidence function in vaccine-induced backward bifurcation in some HIV models

O. Sharomi, C. N. Podder, Abba Gumel, E. H. Elbasha, James Watmough

Research output: Contribution to journalArticle

107 Citations (Scopus)

Abstract

The phenomenon of backward bifurcation in disease models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has important implications for disease control. In such a scenario, the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, condition for disease elimination. This paper addresses the role of the choice of incidence function in a vaccine-induced backward bifurcation in HIV models. Several examples are given where backward bifurcations occur using standard incidence, but not with their equivalents that employ mass action incidence. Furthermore, this result is independent of the type of vaccination program adopted. These results emphasize the need for further work on the incidence functions used in HIV models.

Original languageEnglish (US)
Pages (from-to)436-463
Number of pages28
JournalMathematical Biosciences
Volume210
Issue number2
DOIs
StatePublished - Dec 2007
Externally publishedYes

Fingerprint

Backward Bifurcation
Vaccines
Bifurcation (mathematics)
Vaccine
vaccine
human immunodeficiency virus
bifurcation
Incidence
HIV
vaccines
Reproduction number
incidence
Disease control
Reproduction
disease control
vaccination
Disease Eradication
Endemic Equilibrium
Vaccination
disease models

Keywords

  • AIDS
  • Backward bifurcation
  • Equilibrium
  • HIV
  • Mass action incidence
  • Mathematical model
  • Stability
  • Standard incidence
  • Vaccine

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Role of incidence function in vaccine-induced backward bifurcation in some HIV models. / Sharomi, O.; Podder, C. N.; Gumel, Abba; Elbasha, E. H.; Watmough, James.

In: Mathematical Biosciences, Vol. 210, No. 2, 12.2007, p. 436-463.

Research output: Contribution to journalArticle

Sharomi, O. ; Podder, C. N. ; Gumel, Abba ; Elbasha, E. H. ; Watmough, James. / Role of incidence function in vaccine-induced backward bifurcation in some HIV models. In: Mathematical Biosciences. 2007 ; Vol. 210, No. 2. pp. 436-463.
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