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Journal of Applied Mathematics
Volume 2007, Article ID 17930, 15 pages
http://dx.doi.org/10.1155/2007/17930
Research Article

Boundedness and Large-Time Behavior Results for a Diffusive Epidemic Model

Department of Mathematics, Faculty of Science, University of Batna, Batna 05000, Algeria

Received 7 February 2006; Revised 8 November 2006; Accepted 3 April 2007

Academic Editor: Karl Kunisch

Copyright © 2007 Lamine Melkemi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a reaction-diffusion system modeling the spread of an epidemic disease within a population divided into the susceptible and infective classes. We first consider the question of the uniform boundedness of the solutions for which we give a positive answer. Then we deal with the asymptotic behavior of the solutions where in particular we are interested in reasonable conditions leading to the extinction of the infection disease as the time goes to infinity.