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

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Authors

Garba, Salisu M.
Safi, Mohammad A.
Gumel, Abba B.

Journal Title

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Publisher

Elsevier

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.

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Keywords

Cross-immunity, Multiple strains, Equilibria, Co-existence, Stability

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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.