Global Stability Analysis of a SEIR Epidemic Model with Saturation Incidence Rate

Adebimpe, O. and Moses, B.O. and Okoro, O. J. (2014) Global Stability Analysis of a SEIR Epidemic Model with Saturation Incidence Rate. International Journal of Mathematical Sciences, 34 (1). ISSN 2051-5995

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Abstract

The global stability of a SEIR epidemic model with saturating incidence rate is investigated. A threshold R0 is identified which determines the outcome of the disease. If R0 1 , the infected fraction of the population disappears and the disease dies out while if R0 1 , the infected fraction persists and a unique equilibrium state is shown under a careful restriction of parameters. Dulac’s criterion plus Poincare’-Bendixson theorem and Lyapunov functions are used to prove the global stability of the disease free and endemic equilibria respectively. Numericalsimulation illustrates the main results in the paper. Keywords-SEIR model, saturating incidence rate, global stability, lyapunovfunction, Dulac’s criterion, PoincareBendixson.

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