Mathematical analysis of West Nile virus model with discrete delays

Show simple item record Garba, Salisu M. Safi, Mohammad A. 2013-11-05T06:50:05Z 2013-11-05T06:50:05Z 2013-09
dc.description.abstract The paper presents the basic model for the transmission dynamics of West Nile virus (WNV). The model, which consists of seven mutually-exclusive compartments representing the birds and vector dynamics, has a locally-asymptotically stable disease-free equilibrium whenever the associated reproduction number (R0) is less than unity. As reveal in [3, 20], the analyses of the model show the existence of the phenomenon of backward bifurcation (where the stable diseasefree equilibrium of the model co-exists with a stable endemic equilibrium when the reproduction number of the disease is less than unity). It is shown, that the backward bifurcation phenomenon can be removed by substituting the associated standard incidence function with a mass action incidence. Analysis of the reproduction number of the model shows that, the disease will persist, whenever R0 > 1, and increase in the length of incubation period can help reduce WNV burden in the community if a certain threshold quantities, denoted by Δb and Δv are negative. On the other hand, increasing the length of the incubation period increases disease burden if Δb > 0 and Δv > 0. Furthermore, it is shown that adding time delay to the corresponding autonomous model with standard incidence (considered in [2]) does not alter the qualitative dynamics of the autonomous system (with respect to the elimination or persistence of the disease). en_US
dc.description.librarian hb2013 en_US
dc.description.sponsorship University of Pretoria Research and Development Project (RDP) en_US
dc.description.uri en_US
dc.identifier.citation Garba, SM & Safi, MA 2013, 'Mathematical analysis of West Nile virus model with discrete delays', Acta Mathematica Scientia, vol. 33, no. 5, pp. 1439-1462. en_US
dc.identifier.issn 0252-9602 (print)
dc.identifier.issn 1572-9087 (online)
dc.language.iso en en_US
dc.publisher Springer en_US
dc.rights © Springer-Verlag 2013. The original publication is available at : en_US
dc.subject West Nile virus (WNV) en_US
dc.subject Equilibria en_US
dc.subject Stability en_US
dc.subject Persistent en_US
dc.subject Reproduction number en_US
dc.title Mathematical analysis of West Nile virus model with discrete delays en_US
dc.type Postprint Article en_US

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