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March  2007, 7(2): 365-375. doi: 10.3934/dcdsb.2007.7.365

Uniqueness and stability of positive periodic numerical solution of an epidemic model

Mi-Young Kim 1,

1. 

Department of Mathematics, Inha University, Incheon 402-751, South Korea

Received  January 2006 Revised  October 2006 Published  December 2006

An age structured $s$-$i$-$s$ epidemic model with random diffusion is studied. The model is described by the system of nonlinear and nonlocal integro-differential equations. Finite differences along the characteristics in age-time domain combined with Galerkin finite elements in spatial domain are used in the approximation. It is shown that a positive periodic solution to the discrete system resulting from the approximation can be generated, if the initial condition is fertile. It is proved that the endemic periodic solution is globally stable once it exists.
Keywords: method of characteristics, $s$-$i$-$s$ epidemic model, stability of a periodic solution., random diffusion, integro--differential equation, Galerkin method.
Mathematics Subject Classification: Primary: 65M12, 65M25, 65M60, 92D2.
Citation: Mi-Young Kim. Uniqueness and stability of positive periodic numerical solution of an epidemic model. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 365-375. doi: 10.3934/dcdsb.2007.7.365
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