Time series modelling of tuberculosis disease in Ghana: The Box-Jenkins approach

Abstract

Tuberculosis (TB) disease, in spite being preventable and treatable, is still ranked among the world's major causes of infectious disease-related mortality, killing almost 1.5 million people in 2020 alone. In order to put control measures in place, numerous research have been carried out globally to determine the disease's trend and seasonal variations. “Box-Jenkins method” was employed to analyze monthly TB cases recorded in Ghanaian health facilities between January 2014 and June 2024. The main objective was to find a suitable and economical model to forecast the incidence of the disease. Ten candidate models were identified by the study. The overall best one was chosen using parameter estimation techniques, such as AIC and BIC values. The findings showed seasonal fluctuation and an upward trend in the 126-point TB data. The data was made stationary after first difference and first seasonal difference. SARIMA (1,1,3) (3,1,3)12 was identified as the most effective model for predicting Tuberculosis disease in Ghana following a number of diagnostic tests. The model gave a prediction of monthly TB cases from July 2024 to June 2026. The study concluded that the disease in Ghana showed an upward trend with some seasonal variation but no signs of random fluctuations. The model equation for SARIMA (1,1,3) (3,1,3)12, which was suitable for TB data in Ghana, was; Xt = -0.307Xt-12 + 0.795Xt-24 – 0.250Xt-36 – 2.413Wt-1 + 1.842Wt-2 -0.427Wt-3 + 0.305Wt-12 – 0.794Wt-24 + 0.250Wt-36 + Ѡt