| Summary: | This article analyzes a mathematical model for the dynamics of HIV/AIDS, in which study six behaviors corresponding to five stages of progression of the disease: the phase susceptible, the phase without diagnosis, the phase of diagnosis without viral suppression, with viral suppression and with AIDS, is also considered a protected population under the action of pre-exposure prophylaxis. It is also considered a rate of immigrants in the populations of undiagnosed and diagnosed without viral suppression. With the proposed model, equilibrium points are sought, in which, due to immigration there is no trivial equilibrium point and therefore the basic reproductive number of disease cannot be calculated. Numerical simulations are carried out, and parameters are estimated with data from the city of Pasto, in Colombia, from where it can be seen that timely diagnosis and prevalence in the use of antiretrovirals are very effective in controlling the disease.
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