A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde

We propose a new mathematical model for the transmission dynamics of the human immunodeficiency virus (HIV). Global stability of the unique endemic equilibrium is proved. Then, based on data provided by the “Progress Report on the AIDS response in Cape Verde 2015”, we calibrate our model to the cumulative cases of infection by HIV and AIDS from 1987 to 2014 and we show that our model predicts well such reality. Finally, a sensitivity analysis is done for the case study in Cape Verde. We conclude that the goal of the United Nations to end the AIDS epidemic by 2030 is a nontrivial task.