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.
Lamine Melkemi. Ahmed Zerrouk Mokrane. Amar Youkana. "Boundedness and Large-Time Behavior Results for a Diffusive Epidemic Model." J. Appl. Math. 2007 1 - 15, 2007. https://doi.org/10.1155/2007/17930