The Incidence of Tuberculosis in Brazil from 2001 to 2018: Use of Polynomial Regression Combined with a Stochastic Volatility Model

Monthly tuberculosis (TB) counts from January 2001 to December 2018 showed an upward trend (data from SINAN -Information System for Notifiable Diseases). The increase in the incidence of TB in general is associated with an increase in the rate of extreme poverty, an increase in AIDS cases and other factors. Combining the polynomial linear regression and stochastic volatility models, the purpose of this study was to analyze monthly count data as well as the AIDS/TB, extreme poverty/TB and urban/TB rates associated with the incidence of TB. The results were obtained using the Monte Carlo method in Markov chains under a Bayesian approach. In analyzing the data with the presence of great volatility, despite the growth of TB cases in Brazil, some rates such as AIDS/TB and extreme poverty/TB are decreasing in the same period, indicating that TB cases have increased in the last few years for all sectors of the population of Brazil. The proposed model can be of great use for other epidemiological data, in addition to modeling TB counts and rates associated with TB.