A mathematical study of a tuberculosis model with fractional derivatives

Abstract

In this work, we use a Predictor–Corrector method to implement and derive an iterative solution of an existing Tuberculosis (TB) model with two fractional derivatives, namely, Caputo–Fabrizio fractional derivative and the new generalized Caputo fractional derivative. We begin by recalling some existing results such as the basic reproduction number [Formula: see text] and the equilibrium points of the model. Then, we study the global asymptotic stability of disease-free equilibrium of the fractional models. We also prove, for each fractional model, the existence and uniqueness of solutions. An iterative solution of the two models is computed using the Predictor–Corrector method. Using realistic parameter values, we perform numerical simulations for different values of the fractional order. Simulation results permit to conclude that the new generalized Caputo fractional derivative provides a more realistic analysis than the Caputo–Fabrizio fractional derivative and the classical integer-order TB model.