Mathematical Modeling of the Incidence of Tuberculosis and its Application to the Population of the Mixteca Region of Oaxaca

Abstract

Tuberculosis is caused by Mycobacterium tuberculosis and is primarily transmitted through the air when an infected person coughs, sneezes, or talks, releasing small particles that can infect others they interact with daily. This study aims to present the process of mathematically modelling the disease using information gathered from a bibliographic review. The model is based on differential equations and divides the population into susceptible, latent, infectious, under-treatment, and vaccinated individuals. Using mathematical tools and data provided by health authorities in the Mixteca region, we estimate the model’s parameters and solve it numerically. The numerical solutions provide insights into the incidence of tuberculosis in the Oaxacan Mixteca population, predict future infection rates, and allow for simulations of different scenarios by varying parameter values.