HIV/AIDS Mathematical Model of Triangle Transmission.

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.