AUTHORS: Wirawan Chinviriyasit, Sutawas Janreung, Settapat Chinviriyasit

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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).

KEYWORDS: SEIRS epidemic model, Nonlinear incidence rate, Backward bifurcation

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