Acquired Immune Deficiency Syndrome (AIDS) was first found in the United States in
1981, which was characterized by a deterioration of the immune system. In 1983,
scientists from the Institut Pasteur, France, and the National Institute of Health, USA,
showed that a virus was the cause of AIDS, which was then called the human
immunodeficiency virus (HIV). The HIV/AIDS has an increasing number of infectious
each year in the city of Castanhal, in this sense we chose to analyze the study of cases of
infected from real data of HIV/AIDS made available by CEADIC/Castanhal-PA, between
2000 and 2013, this work proposes through the deterministic epidemiological model SI
(susceptible, infected), model and solve, through the numerical methods of Taylor Series
and Runge-Kutta, both of 2nd order, analyze the convergence of the proposed numerical
solutions and calculate their predictive estimates, both infected and susceptible in the
municipality of Castanhal. With the analyses, we verified that the numerical solutions are
close to the real data of infected and susceptible people, thus we are facing the validation
of the application of the deterministic epidemiological model SI (susceptible, infected) when solved through both proposed numerical methodologies (Taylor Series and Runge-
Kutta).
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