A Local Analysis of a Mathematical Pattern for Interactions between the Human Immune System and a Pathogenic Agent

In the present study, we introduce a four-dimensional deterministic mathematical pattern in order to study the interactions between the human immune system and a virus. The model is based on a system with four first-order ordinary differential equations, and the main aim of the paper is to perform a mathematical analysis of the local behavior of the associated dynamical system using the tools of the qualitative theory of dynamical systems. Moreover, two types of patterns with controls were introduced; consequently, some very interesting theoretical conclusions with medical relevance were obtained.

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

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.