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Stability Analysis of SIQS Epidemic Model with Saturated Incidence Rate
Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria
Department of Mathematics, Tai Solarin University of Education, Ijebu-Ode, Nigeria
Department of Mathematical and Physical Science, Osun State University, Osogbo, Nigeria
- 1 Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria
- 2 Department of Mathematics, Tai Solarin University of Education, Ijebu-Ode, Nigeria
- 3 Department of Mathematical and Physical Science, Osun State University, Osogbo, Nigeria
Applied Mathematics·Volume 07 (2016)·Pages 1082–1086·Published 7 June 2016·DOI10.4236/am.2016.710096
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Abstract
A SIQS epidemic model with saturated incidence rate is studied. Two equilibrium points exist for the system, disease-free and endemic equilibrium. The stability of the disease-free equilibrium and endemic equilibrium exists when the basic reproduction number R0, is less or greater than unity respectively. The global stability of the disease-free and endemic equilibrium is proved using Lyapunov functions and Poincare-Bendixson theorem plus Dulac’s criterion respectively.
KeywordsSIQS Epidemic ModelSaturated Incidence RateBasic Reproduction NumberLyapunov FunctionPoincare-BendixsonDulac Criterion
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