  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.
