A multi-scale mathematical model is proposed, seeking to describe the propagation of Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through unprotected sexual contact. The uses of antiretroviral therapy (ART) and therapeutic failure are considered to show how the rate of propagation and prevalence are affected. The model consists of a complex network modeling the interactions on the population scale, coupled with the immunological dynamics of each individual, which is modeled by a system of differential equations. The immunological model allows to observe some known facts from the literature, such as to control HIV infection in the immune system, it is necessary to reduce the probability of healthy CD4 T cells becoming infected or increase the probability at which cells of the specific cell response against HIV eliminate infected CD4 T cells. At the population level, it is shown that, to have a high prevalence, it is not necessary for the virus to spread rapidly at the beginning of the simulation time. Additionally, it is observed that a greater number of sexual partners induces higher HIV prevalence. Using ART in the immune system reduces the number of infected CD4 T cells and, consequently, helps to reduce the spread of infection at the population scale. An important result observed in simulations is that the average number of HIV carriers who abandon ART is greater than those who access it. The study adds to the available literature an original simulation model that describes the dynamics of HIV propagation in a population, considering the immune state of people within that population, and serves as a basis for future research involving more detailed aspects aiming for a model closest to reality.

A multiscale mathematical model is proposed seeking to study the propagation dynamics of the Human Immunodeficiency Virus (HIV) in a group of young people between 15 and 24 years of age, through sexual contact without protection, considering the use of antiretroviral therapy (ART) and therapeutic failure. The model consists in a scale-free complex network that follows a power law, coupled with the immunological dynamics of each individual, that is, it considers the infection by the virus in the immune system of each HIV carrier, through a system of non-linear differential equations that govern the infection’s behavior in the immune system. Propagation of the virus in the network is modelled by taking into account information from the immunological status of each person. The study found that for a population to have high HIV prevalence, it is not necessary at the beginning of the simulation time for the virus to propagate rapidly. In addition, the study proves that with a higher number of sexual partners, there will be greater prevalence of HIV in the population and that the use of ART helps to control the propagation of the infection in the population. As an interesting result, it was also found that there is a higher number of HIV carriers who abandon ART than those who have access to it.