Aplicação dos métodos numéricos série de Taylor e Runge - Kutta na solução do modelo epidemiológico determinístico SI (suscetíveis - infectados) sobre os dados reais da tuberculose no município Codó - MA entre os anos 2001 e 2014

Abstract

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.