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

Journal of Mathematical Biology
David Greenhalgh, Martin Griffiths

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.

References

Jul 1, 1995·Mathematical Biosciences·K P Hadeler, C Castillo-Chavez
Jun 7, 1996·Journal of Theoretical Biology·J Dushoff
Nov 14, 1997·Mathematical Biosciences·K P Hadeler, P van den Driessche
Jul 10, 1999·IMA Journal of Mathematics Applied in Medicine and Biology·Q J Khan, D Greenhalgh
Aug 17, 2000·Journal of Mathematical Biology·P van den Driessche, J Watmough

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Citations

Aug 3, 2013·Mathematical Biosciences and Engineering : MBE·Deborah Lacitignola
Sep 6, 2012·Journal of Mathematical Biology·Muntaser SafanKarl P Hadeler
Apr 21, 2012·Mathematical Biosciences·Zhixing HuShigui Ruan
Mar 8, 2011·Mathematical Biosciences·Martin Griffiths, David Greenhalgh
Sep 25, 2010·Journal of Theoretical Biology·S A Pedro, J M Tchuenche
Mar 20, 2010·Mathematical Biosciences·Farai Nyabadza, Senelani D Hove-Musekwa
Aug 18, 2009·Mathematical Biosciences·David Greenhalgh, Martin Griffiths
Apr 25, 2015·Journal of Theoretical Biology·Ani AsatryanNatalia L Komarova
Mar 23, 2018·PloS One·Isaac Mwangi Wangari, Lewi Stone
Jun 8, 2017·Journal of Mathematical Biology·Hamadjam AbboubakarDaniel Tieudjo

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