Causes of backward bifurcations in some epidemiological models

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

The phenomenon of backward bifurcation in disease transmission models, where a stable endemic equilibrium co-exists with a stable disease-free equilibrium when the associated reproduction number is less than unity, has been observed in a number of disease transmission models. The epidemiological consequence of backward bifurcation is that the classical requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, for disease elimination (hence, the presence of this phenomenon in the transmission dynamics of a disease makes its effective control in the community difficult). This paper addresses the problem of finding the causes of backward bifurcation in some standard deterministic models for the spread of some emerging and re-emerging diseases (it contains a brief review of some common causes, as well as some new causes, of backward bifurcation in some standard disease transmission models). It is shown that, in addition to the usual causes (such as the use of imperfect vaccine and exogenous re-infection in TB disease), a number of other biological or epidemiological mechanisms, such as vaccine-derived immunity waning at a slower rate than natural immunity, disease-induced mortality in vector-borne diseases and differential susceptibility in risk-structured models, could also cause backward bifurcation in disease transmission models.

Original languageEnglish (US)
Pages (from-to)355-365
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume395
Issue number1
DOIs
StatePublished - Nov 1 2012
Externally publishedYes

Fingerprint

Backward Bifurcation
Epidemiological Model
Reproduction number
Vaccines
Vaccine
Immunity
Model
Endemic Equilibrium
Bifurcation (mathematics)
Deterministic Model
Mortality
Imperfect
Susceptibility
Infection
Elimination
Standard Model

Keywords

  • Backward bifurcation
  • Equilibrium
  • Reproduction number
  • Stability
  • Standard incidence

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Causes of backward bifurcations in some epidemiological models. / Gumel, Abba.

In: Journal of Mathematical Analysis and Applications, Vol. 395, No. 1, 01.11.2012, p. 355-365.

Research output: Contribution to journalArticle

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