Journal of Applied Mathematics 
Volume 2007 (2007), Article ID 17930, 15 pages
doi:10.1155/2007/17930
Research Article

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

Lamine Melkemi, Ahmed Zerrouk Mokrane, and Amar Youkana

 Department of Mathematics, Faculty of Science, University of Batna, Batna 05000, Algeria
Received 7 February 2006; Revised 8 November 2006; Accepted 3 April 2007

Recommended by Karl Kunisch

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.