International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 638021, 8 pages
doi:10.1155/2010/638021
Research Article

Dynamics and Thresholds of a Simple Epidemiological Model: Example of HIV/AIDS in Mali

Ouaténi Diallo,1 Yaya Koné,1 and Jérôme Pousin2

1Département de Mathématiques et D'Informatique, Faculté des Sciences et Techniques, B.P.E 3206, Bamako, Mali
2Université de Lyon, INSA, ICJ UMR CNRS 5208, 69100 Lyon, France

Received 23 March 2010; Revised 13 August 2010; Accepted 23 September 2010

Academic Editor: Thomas Witelski

Copyright © 2010 Ouaténi Diallo 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

The dynamics of many epidemiological models for infectious diseases that spread in the sexually active population presents a crucial period: the period of the influx or recruitment of susceptible. In this paper, we assume that the recruitment of susceptible is done among the juvenile group. We propose a dynamical system to modelize the disease spread, and we study the dynamical behavior of this system. Then, the controllability of the system is studied. We prove that the survival rate allows to control the dynamic of the system. Numerical simulations are given to illustrate the results.