BASIC EPIDEMIOLOGICAL MODELS IN A PROPOSAL FOR THE TEMPORAL EVOLUTION OF AIDS

Abstract

From the 80's to the present day, there has been great progress in research regarding the diagnosis, treatment and control of AIDS, but this disease still affects the Brazilian population with intensity. The HIV virus acts on the immune system, leading to the emergence of opportunistic diseases. Antiretroviral therapies allowed patients to maintain a healthy life for a long time. However, some recent research has shown that this virus may be responsible for premature aging of infected people, causing the degenerative character of the disease to be widely discussed. Just as health scholars have been researching how to contain this syndrome more effectively, mathematicians have developed some epidemiological models, formed by systems of ordinary nonlinear differential equations. Therefore, mathematical modeling has been an important tool in Epidemiology. The basis of our studies on the evolution of AIDS begins with a system, representative of the IS model, built for the city of Manaus, capital of Amazonas, between 2009 and 2014. For this, we carried out a bibliographic survey on the basic models SI, SIS, SIR, SIRS and SIRV, analyzed the criteria for the stability of the critical points, in addition to observing the behavior of the graphs generated by the temporal evolutions, built in the Octave software. With this, we are able to make some predictions about the number of infected, susceptible, or even how many would be recovered or vaccinated, in this process of evolution. We will start from the simplest model, where there is no form of recovery, until the conclusion of the studies with the post-vaccination model.

DOI: https://doi.org/10.56238/sevened2024.042-008