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.
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.