Backward bifurcation, equilibrium and stability phenomena in a three-stage extended BRSV epidemic model

D. Greenhalgh, M. Griffiths

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

In this paper we consider the phenomenon of backward bifurcation in epidemic modelling illustrated by an extended model for Bovine Respiratory Syncytial Virus (BRSV) amongst cattle. In its simplest form, backward bifurcation in epidemic models usually implies the existence of two subcritical endemic equilibria for R 0 < 1, where R 0 is the basic reproductive number, and a unique supercritical endemic equilibrium for R 0 > 1. In our three-stage extended model we find that more complex bifurcation diagrams are possible. The paper starts with a review of some of the previous work on backward bifurcation then describes our three-stage model. We give equilibrium and stability results, and also provide some biological motivation for the model being studied. It is shown that backward bifurcation can occur in the three-stage model for small b, where b is the common per capita birth and death rate. We are able to classify the possible bifurcation diagrams. Some realistic numerical examples are discussed at the end of the paper, both for b small and for larger values of b.
LanguageEnglish
Pages1-36
Number of pages36
JournalJournal of Mathematical Biology
Volume59
Issue number1
DOIs
Publication statusPublished - Jul 2009

Fingerprint

Bovine respiratory syncytial virus
Backward Bifurcation
Epidemic Model
Viruses
Virus
Biological Models
Birth Rate
Endemic Equilibrium
Bifurcation Diagram
Mortality
Basic Reproductive number
Model
birth rate
Classify
Imply
Numerical Examples
Modeling
cattle

Keywords

  • backward bifurcation
  • equilibrium and stability analysis
  • basic reproduction ratio
  • simulation
  • three stage model
  • bovine respiratory syncytial virus

Cite this

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Backward bifurcation, equilibrium and stability phenomena in a three-stage extended BRSV epidemic model. / Greenhalgh, D.; Griffiths, M.

In: Journal of Mathematical Biology, Vol. 59, No. 1, 07.2009, p. 1-36.

Research output: Contribution to journalArticle

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