Analysis And Assessment Of Tuberculosis Epidemiology Dynamics With A Compartment Based Mathematical Model

Abstract

Tuberculosis (TB) is an airborne infectious disease caused by Mycobacterium tuberculosis that has co-evolved with humanity. Its strategy for success consists of remaining almost hidden and acting slowly. The Global Tuberculosis Report 2015 from the World Health Organization (WHO) estimates that, in 2014, 9.6 million people developed TB and 1.5 million died as a consequence of the disease. According to the report of the Public Health Agency of Barcelona (ASPB), in 2014 were detected 300 cases of tuberculosis in Barcelona residents, equivalent to an incidence rate of 18.6 cases per 100,000 inhabitants. The highest TB incidence in Barcelona is found in the Ciutat Vella neighbourhood. We have observed that the behaviour of most of the countries can be adjusted to parabolic functions, while other functions, such as exponentials, show worst adjustments. For this reason, we have developed a program to automatically adjust a parabolic function to epidemiological data retrieved from the WHO’s database. The adjustments obtained provided a first overview of the epidemiological situation of each country and stated that the most frequent behaviour observed was of a decreasing type. The regularities observed, in countries with very different situations, should be explained by the behaviour of the disease. For this purpose, a mathematical model was developed with the aim to describe the dynamics observed in TB epidemiology. Although simple, the model is robust and allows the study the dynamics of the disease and to make medium and long-term predictions of the evolution of TB disease under different circumstances. The mathematical model was properly adjusted for several countries and also to the city of Barcelona. The mathematical model has allowed to define a parameter (q) that can be used to evaluate the quality of TB control programs.

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