A fractal-fractional mathematical model for COVID-19 and tuberculosis using Atangana–Baleanu derivative

This study aims to develop a compartmental epidemiological model for the co-infection of COVID-19 and tuberculosis, incorporating a Holling type II treatment rate for individuals with tuberculosis, COVID-19, and dual infections while considering incomplete treatment in some TB cases. The model analysis examines the sub-models for COVID-19, TB, and the combined co-infection model. Using the fixed-point method, the research investigates the existence and uniqueness of solutions for the proposed model. It also explores a stability analysis to evaluate Ulam-Hyer’s reliability. Furthermore, it discusses and validates Lagrange’s interpolation polynomial through a specific case study to numerically compare different fractal and fractional orders.