DIRECT (SI) AND INDIRECT (SLI) PROGRESSIONS IN A MODEL FOR THE TUBERCULOSIS EPIDEMIC

Abstract

Mathematical modeling is fundamental for investigating the spread of an infectious disease. The dynamics between compartments are studied by researchers, who have an important mission in Epidemiology, which is to make predictions based on evolution charts and the numerical data obtained. The continuous transfer between these groups of individuals organized into compartments can represent cases of infection, situations of permanent or temporary recovery from the disease. The Tuberculosis model presented in this article is expressed by a system of nonlinear ordinary differential equations. The dynamics between the compartments can be organized into two stages: direct progression (SI model) and indirect progression (SLI model). The complete model contains both types of progressions. We will initially study the direct progression and later complement it with the indirect one. The inclusion of the complete model alters the total number of people in the sick categories. Susceptible individuals may develop tuberculosis quickly or not at all. Thus, we have four categories of individuals: susceptible, latent, infected with pulmonary tuberculosis, and infected with extrapulmonary tuberculosis. Individuals who reach the latent category can be transferred to the infected categories and, once cured, return to the group. Our goal will be to perform numerical simulations, assigning values to the parameters, analyzing the effects caused by changes in this data, and making predictions. We will use the effective reproductive rate to help forecast when the disease spreads among the population and when it is eradicated.