The probability of extinction in a bovine respiratory syncytial virus epidemic model

Martin Griffiths, David Greenhalgh

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Backward bifurcation is a relatively recent yet well-studied phenomenon associated with deterministic epidemic models. It allows for the presence of multiple subcritical endemic equilibria, and is generally found only in models possessing a reasonable degree of complexity. One particular aspect of backward bifurcation that appears to have been virtually overlooked in the literature is the potential influence its presence might have on the behaviour of any analogous stochastic model. Indeed, the primary aim of this paper is to investigate this possibility. Our approach is to compare the theoretical probabilities of extinction, calculated via a particular stochastic formulation of a deterministic model exhibiting backward bifurcation, with those obtained from a series of stochastic simulations. We have found some interesting links in the behaviour between the deterministic and stochastic models, and are able to offer plausible explanations for our observations.
LanguageEnglish
Pages144-158
Number of pages15
JournalMathematical Biosciences
Volume231
Issue number2
DOIs
Publication statusPublished - Jun 2011

Fingerprint

Bovine respiratory syncytial virus
Backward Bifurcation
Epidemic Model
Deterministic Model
Viruses
Extinction
Virus
extinction
Stochastic models
Stochastic Model
Multiple Equilibria
Endemic Equilibrium
Stochastic Simulation
Series
Formulation
Model

Keywords

  • backward bifurcation
  • branching process
  • stochastic simulation
  • probabilities of extinction
  • stochastic model
  • deterministic model

Cite this

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The probability of extinction in a bovine respiratory syncytial virus epidemic model. / Griffiths, Martin; Greenhalgh, David.

In: Mathematical Biosciences, Vol. 231, No. 2, 06.2011, p. 144-158.

Research output: Contribution to journalArticle

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