AN EVOLUTION TOWARDS AIDS WITH BASIC EPIDEMIOLOGICAL MODELS

Abstract

The HIV virus harms the immune system, facilitating the onset of opportunistic diseases. This system's mission is to defend our body against different agents. In the case of AIDS, some of the patient's defense cells are attacked and destroyed. Antiretroviral therapies mitigate this process, allowing people to lead a healthy life. Numerous researchers are involved in the search for more effective treatment and control, and some mathematicians have developed epidemiological models. Mathematical modeling has advanced in building increasingly complex models that address the specific characteristics of each disease. To understand this process, it is useful to start with simpler models. We will begin with the SI model, developed for the city of Manaus, the capital of Amazonas, between 2009 and 2014. For this, we conducted a literature review on the basic models SI, SIS, SIR, SEIR, SECIAR and present a proposal to include a vaccine for  susceptibles. With this, we became able to make some predictions about the percentages of infected, susceptible, recovered, vaccinated, and others, based on the graphs built in Octave. We can see that when we include a possibility of recovery, the number of infected people grows, but reaches a maximum and then starts to decrease until they disappear after a certain period. With vaccination, on the other hand, we can reduce the maximum percentage reached by the infected.