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

Greenhalgh, D. and Griffiths, M. (2009) Backward bifurcation, equilibrium and stability phenomena in a three-stage extended BRSV epidemic model. Journal of Mathematical Biology, 59 (1). pp. 1-36. ISSN 0303-6812

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    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.

    Item type: Article
    ID code: 14032
    Keywords: backward bifurcation, equilibrium and stability analysis, basic reproduction ratio, simulation, three stage model, bovine respiratory syncytial virus, Mathematics
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science
    Related URLs:
      Depositing user: Mrs Ann Lynch
      Date Deposited: 08 Jan 2010 17:29
      Last modified: 11 Oct 2012 22:55
      URI: http://strathprints.strath.ac.uk/id/eprint/14032

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