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

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