A Mathematical Model for HIV/AIDS Under Pre-Exposure and Post-Exposure Prophylaxis.

HIV/AIDS has a strong impact on society, the economy, and health. Early diagnosis of cases, adherence to treatment, and prevention are important factors in controlling the epidemic in the population. In this paper, we present a new mathematical model for the study of HIV/AIDS transmission. Our model is stratified in men and women, to account for the main forms of sexual transmission homosexual and heterosexual relationships, and infectiousness in the HIV and AIDS stages. In addition, in the construction of the model, we take into account the influence of Pre-Exposure Prophylaxis (PrEP) and Post-Exposure Prophylaxis (PEP) to study the impact of these implementations, diagnosis, and effectiveness of treatment based on viral load undetectability. We study the basic reproduction number by subpopulation (men and women) and general. Working by subpopulations allows us to study men who have sex with men who have a strong impact on virus transmission. Also, we study the infection-free equilibrium points due to their relationship with the basic reproduction number and demonstrate the global stability by subpopulation and general. To explore our model, we performed computational simulations on. [ABSTRACT FROM AUTHOR]