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

Martin Griffiths, David Greenhalgh

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)144-158
Number of pages15
JournalMathematical Biosciences
Issue number2
Publication statusPublished - Jun 2011


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


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