Dynamics and thresholds of a simple epidemiological model: example of HIV/AIDS in mali (Q610808)

Summary: 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 susceptibles. In this paper, we assume that the recruitment of susceptibles 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.