Cross-immunity-induced backward bifurcation for a model of transmission dynamics of two strains of influenza

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dc.contributor.author Garba, Salisu M.
dc.contributor.author Safi, Mohammad A.
dc.contributor.author Gumel, A.B.
dc.date.accessioned 2013-02-20T06:58:49Z
dc.date.available 2013-02-20T06:58:49Z
dc.date.issued 2013-06
dc.description.abstract A new deterministic model for the transmission dynamics of two strains of in- uenza is designed and used to qualitatively assess the role of cross-immunity on the transmission process. It is shown that incomplete cross-immunity could in- duce the phenomenon of backward bifurcation when the associated reproduction number is less than unity. The model undergoes competitive exclusion (where Strain i drives out Strain j to extinction whenever R0i > 1 > R0j ; i; j = 1; 2; i ̸= j). For the case where infection with one strain confers complete im- munity against infection with the other strain, it is shown that the disease-free equilibrium of the model is globally-asymptotically stable whenever the repro- duction number is less than unity. In the absence of cross-immunity, the model can have a continuum of co-existence endemic equilibria (which is shown to be globally-asymptotically stable for a special case). When infection with one strain confers incomplete immunity against the other. Numerical simulations of the model show that the two strains co-exist, with Strain i dominating (but not driving out Strain j), whenever R0i > R0j > 1. en_US
dc.description.librarian am2013 en_US
dc.description.uri http://www.elsevier.com/locate/nonrwa en_US
dc.identifier.citation Garba, SM, Safi, MA & Gumel, AB 2013, 'Cross-immunity-induced backward bifurcation for a model of transmission dynamics of two strains of influenza', Nonlinear Analysis: Real World Applications, vol. 14, no. 3, pp. 1384-1403. en_US
dc.identifier.issn 1468-1218
dc.identifier.other 10.1016/j.nonrwa.2012.10.003
dc.identifier.uri http://hdl.handle.net/2263/21129
dc.language.iso en en_US
dc.publisher Elsevier en_US
dc.rights © 2012 Elsevier. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Nonlinear Analysis: Real World Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis: Real World Applications, vol. 14, issue 3, 2013, doi: 10.1016/j.nonrwa.2012.10.003. en_US
dc.subject Cross-immunity en_US
dc.subject Multiple strains en_US
dc.subject Equilibria en_US
dc.subject Co-existence en_US
dc.subject Stability en_US
dc.title Cross-immunity-induced backward bifurcation for a model of transmission dynamics of two strains of influenza en_US
dc.type Postprint Article en_US


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