Dinâmica epidemiológica da aids

Abstract

The Acquired Immunodeficiency Syndrome (AIDS), caused by the HIV virus, has arisen strong interest since first detections in 1981. The virus was isolated for first time in 1983 in France and since then public policies have been put in place to minimize the reach of the disease. The virus invades the immune system and attacks the cells responsible for our defense, thus, the individual becomes susceptible to the action of other diseases. The body presents a very complex barrier, which daily combats attacks by bacteria, viruses and other microbes, composed of millions of cells of different types and different functions, among the defense cells are the TCD4 + lymphocytes, the main targets of HIV. Antiretroviral drugs (ARVs) emerged in the 1980s and began to be implemented in Brazil in 1996, their main objectives are to prevent HIV transmission and keep the health of individuals stable, since antiretroviral drugs reduce the amount of circulating virus in the individual’s body. In order to develop a work focused on the characteristics of the country, it is relevant to promote a study on population dynamics and consider its characteristics in the model adopted. Thus, this work consists of proposing a new mathematical model, constituted by a system of Ordinary Differential Equations, which allows to understand, over time, the epidemiological evolution of the AIDS disease in the human population, with the understanding of the stages by which the susceptible individual , when in contact with the virus, it will go from contraction to the effective development of AIDS. The proposed model is compartmentalized and of the SLI type, in which the populations are divided into susceptible, latent and infected, and also differentiates the disease between men and women, keeping each of these populations constant over time.For both models, the disease-free and endemic equilibrium points are determined and the stability study for these points is made. In first model proposed, which takes into account only infection among people of the opposite sex, the local stability of the disease-free and endemic equilibrium points was analyzed and the global stability is obtained through Lyapunov functional for disease-free equilibrium point. In the second model, which also deals with the transmission of men to men, only R0 was obtained and the study of the local stability of the disease-free point. The simulations were performed with the R software using real data, which allow us to conclude that the model is appropriate for this type of study. In addition, simulations for other scenarios were performed and the models corroborate the qualitative analyzes obtained by looking at different of R0.