Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia

Abstract

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 benefits 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.

Keywords: antiretroviral therapy; human immunodeficiency virus; system of ordinary differential equations.

FIG. 1.

Triangle transmission between homosexual men, heterosexual men, and women.

FIG. 2.

Diagram and ODE system for triangle transmission model. ODE, ordinary differential equations.

FIG. 3.

Bifurcation diagram of untreated infected heterosexual men, in function of transmission probability in homosexual contact.

FIG. 4.

On the left, the main scenario using parameters in table description of parameters. On the right, disease-free equilibrium when the basic reproduction number in homosexuals is less than one, both in logarithm scale.

FIG. 5.

Scenario 1: modifying heterosexual partners’ rate.

FIG. 6.

Scenario 2: modifying departure rate from infected individuals.

FIG. 7.

Scenario 3: modifying bisexual partner.