Qualitative analysis of HAART effects on HIV and SARS-CoV-2 coinfection

HIV is known for causing the destruction of the immune system by affecting different types of cells, while SARS-CoV-2 is an extremely contagious virus that leads to the development of COVID-19. In this study, we propose a mathematical model to investigate the interaction between HIV and SARS-CoV-2 under highly active antiretroviral therapy (HAART). We determine the conditions for the endemic equilibria of both viruses, showing that transcritical bifurcations occur when the basic reproduction numbers of HIV and SARS-CoV-2 pass through 1. We set the condition for the stability of the disease-free equilibrium point of the model with coinfection as a function of the basic reproduction number $\mathcal{R}_0$. Through numerical simulations, we conclude that HAART, used to control HIV, also reduces the proliferation of SARS-CoV-2-infected cells in coinfected hosts. These findings provide important insights into the epidemiological dynamics of HIV and SARS-CoV-2 coinfection.