Mathematical Modeling of the Epidemiology of Tuberculosis in the Ashanti Region of Ghana

Abstract

Tuberculosis is an infectious disease which can be fatal. Hence, availability of models predicting its potential outbreak can be very useful in its preventative strategies. This paper finds the best mathematical model which fits onto the tuberculosis occurrence data of Ashanti Region of Ghana, and uses the model to predict the future epidemiology and incidence of the disease in the region to enhance anti-tuberculosis campaigns. The data used for the study was obtained from the Ashanti Health Services and spans January 2001 to March 2013. It is evident from the analysis that tuberculosis occurrence in the region studied can best be modeled with ARMA (1, 0) or AR(1), i.e. a stochastic time series linear model, and that tuberculosis epidemic in the Ashanti Region is expected to be stable between April 2013 and April 2015. The Mean Absolute Error (MAE) and the Mean Squared Error (MSE) are used to compare the in-sample forecasting performance of three selected competing models, and the result shows that it is not always true that the best selected model gives the best results so far as the mean square error (MSE) is concerned. The forecasting accuracies for the obtained model, i.e. AR (1), using MAE and MSE are respectively 16.3171 and 461.3148.