The Impact of Caputo Fractional Derivative on Mathematical Modeling of Tuberculosis Disease

Abstract

Memory effect, one of the most important advantages of fractional derivative and integral operators, is a prominent characteristic of a disease. Mycobacterium tuberculosis is one of such memory-dependent precarious disease that affects the lungs. Therefore, we investigate this serious public health infection by means of the Caputo operator having memory. Firstly, some fundamental features of the proposed model such as the positiveness of solutions, the disease-free equilibrium, and endemic equilibrium points are presented. Then, the basic reproduction number to characterize the disease model under consideration is calculated. In addition, stability analysis is performed by using these basic calculations, and comments are made on the course of the tuberculosis infection. On the other hand, we numerical simulations in order to show the effect of non- integer order on the mycobacterium tuberculosis transmission are carried out. Lastly, comparison analysis between the classical and fractional mathematical models is supported by various graphs. The results show that fractional order can greatly affect the course of the tuberculosis transmission and allow for more specific predictions about this global health issue.