Fractal-fractional model for analysis of tuberculosis infection using Ethiopia incidence data

In this study, a fractional-order $SE{I}_{u}ITR$ model was proposed to examine the transmission of tuberculosis (TB) in the community. The proposed model was rigorously examined for well-posedness. The basic reproduction number was also derived, and the disease-free equilibrium was obtained. The local and global stabilities of the proposed model were also examined. The proposed model was fitted with the actual TB incidence in Ethiopia, while numerical simulations were carried out in MATLAB to validate the results obtained in this study. Local and global sensitivity analyses were carried out to determine the key parameters that influence the transmission of TB in the community. Phase-plane portraits and phase-plane diagrams demonstrate the dynamic process of the state variables. The results indicate that as the fractional-order increases, the number of infections decreases due to the memory effect of early detection and treatment, while as the order decreases, the number of infections increases. Early detection and treatment have a profound effect on recovery and prevalence.