WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 17, 2018
On the Backward Bifurcation of an SEIRS Epidemic Model with Nonlinear Incidence Rate
Authors: , ,
Abstract: An SEIRS epidemic model with a nonlinear incidence rate is investigated. Mathematical analysis reveals that the model has a locally asymptotically stable disease–free equilibrium (DFE) whenever a certain epidemiological threshold, known as the basic reproduction number R0, is less than unity. Using the theory of centre manifold, the model exhibits the phenomenon of backward bifurcation, where the stable DFE coexists with a stable endemic equilibrium when R0 < 1. The epidemiological consequence of this phenomenon is that the classical epidemiological requirement of the reproduction number being less than unity becomes only a necessary, but not sufficient, for disease elimination (hence, the presence of this phenomenon in the transmission dynamics of a disease makes its effective control in the community difficult).
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Pages: 221-227
WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 17, 2018, Art. #24