Tuberculosis is usually caused by an infection with Mycobacterium tuberculosis or
Koch's Bacillus. The treatment of tuberculosis is based on antibiotics and leads to a
cure, provided that treatment is not abandoned (MARCOLINO, 2016). Based on real
tuberculosis data provided by SINAM/Codó-MA between 2001 and 2014
(MARCOLINO, 2016), this work proposes, through the deterministic epidemiological
model SI (susceptible, infected), to model and solve, through numerical methods from
the Taylor and Runge-Kutta series, both of 2nd order, to analyze the convergence of
the proposed numerical solutions and calculate their forecast estimates, both of
infected and susceptible in the city of Codó-MA. We observed that the numerical
solutions of infected and susceptible, by (Taylor and Runge-Kutta series), are as close
to each other as to the real data of infected and susceptible respectively. We found
that these numerical solutions of infected decrease and susceptible increase both in a
polynomial way. From 2014 onwards, it is possible to estimate forecasts through
numerical solutions for both infected and susceptible individuals.
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