While several studies on human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS) in the homosexual and heterosexual population have demonstrated substantial advantages in controlling HIV transmission in these groups, the overall 2benefits of the models with a bisexual population and initiation of antiretroviral therapy have not had enough attention in dynamic modeling. Thus, we used a mathematical model based on studying the impacts of bisexual behavior in a global community developed in the PhD thesis work of Espitia ( 2021 ). The model is governed by a nonlinear ordinary differential equation system, the parameters of which are calibrated with data from the cumulative cases of HIV infection and AIDS reported in San Juan de Pasto in 2019. Our model estimations show which parameters are the most influential and how to modulate them to decrease the HIV infection.

In this paper, a mathematical analysis of the HIV/AIDS deterministic model studied in the paper called Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a case study in the previous works preformed by Espitia is performed. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness; the calculus of the basic reproduction number; stationary points such as disease-free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE); and the local stability (LAS) of disease-free equilibrium. The findings allow us to conclude that the best way to reduce contagion and consequently reach a DFE is thought to be the reduction in the rate of homosexual partners, as they are the most affected population by the virus and are therefore the most likely to become infected and spread it. Increasing the departure rate of infected individuals leads to a decrease in untreated infected heterosexual men and untreated infected women.