Fractional dynamics of a Tuberculosis model

The aim of this work is to formulate and analyze a deterministic model for the transmission dynamics of tuberculosis in the Adamaoua region of Cameroon, in which we take into account both pulmonary and extrapulmonary tuberculosis, and using fractional-order derivative in the Caputo sense. After showing the existence and uniqueness of solutions, we calculate the basic reproduction number R 0 , and study the stability of the tuberculosis-free equilibrium point when R 0 < 1. Then we show the existence of at least one endemic equilibrium point when R 0 > 1. Using data from Adamaoua, we calibrate the model by estimating certain parameters. We thus estimate the value of the basic reproduction number R 0 = 4.1683, which means that tuberculosis is endemic in the Adamaoua region since R 0 > 1. We then perform numerical simulations to validate the theoretical results.