Dynamical Analysis of a Tuberculosis Model using Fractal-Fractional Operator

In this article, tuberculosis dynamics is studied using the fractal-fractional (FF) operator in the Caputo-Fabrizio (CF) sense. To understand the transmission dynamics of tuberculosis in India and to investigate the possibility of achieving tuberculosis eradication within the shortest possible time frame, a five-compartment mathematical model is presented. The entire tuberculosis-infected population is categorized into three groups, namely drug-sensitive (DS), multidrug-resistant (MDR), and isolated classes. The existence and uniqueness of the model governed by the CFFF derivative are established through the application of fixed-point theorems. The Ulam-Hyers stability of the model is examined using nonlinear analysis. Numerical solutions of the proposed model are obtained through the development of the Adams-Bashforth method. Based on the numerical simulations, it is suggested that tuberculosis could be eradicated in India if a high treatment success rate is achieved and at least 50% of MDR-TB cases are isolated.