ABSTRACT :

The HIV/AIDS model was dynamically analyzed in this study. The model has seven compartments: the uneducated, the educated, the HIV-positive who take antiretroviral therapy (ART), the HIV-positive who do not take ART, people receiving ART treatment, people with AIDS
who do not receive any treatment (full-blown AIDS), and the recovered. This model takes
into account the analysis of the multiple interactions between the uneducated and the educated subpopulations, the HIV-positive who take and who do not take ART. The free-disease
and endemic equilibrium points, as well as the basic reproduction number ðR0Þ as a limit
condition for infection-free and endemic occurrence, were produced by a mathematical analysis. The center-manifold hypothesis was used to prove that a backward bifurcation exists.
The free-disease and endemic equilibrium points coexist when R0 < 1: This means that HIV/
AIDS is still spreading. A basic reproduction number below one is insufficient to constitute a
free-disease condition. In order to determine essential parameters that significantly contribute to HIV/AIDS transmission, we computed sensitivity index values using a sensitivity analysis. The HIV/AIDS model and bifurcation parameter both identified the rate of HIV
transmission from uneducated individuals to HIV-positive individuals who do not receive
ART as the most crucial parameter. A numerical simulation supports the dynamical analysis.