A fractional order model for transmission dynamics of TB with funding-driven vaccination and social processes

This study highlights the role of human preventive behavior, positive attitudes towards hospital-based treatment, and funding of vaccination programs in understanding the transmission dynamics of tuberculosis. To effectively account for human experiences, a Caputo-based fractional-order mathematical model is formulated. The well-posedness of the proposed model is examined using the Generalized Mean Value Theorem, Mittag-Leffler functions, and the Banach contraction mapping principle. To examine the robustness of the solutions, the Ulam–Hyers approach is employed. The next-generation matrix technique is adopted to derive the socioeconomic reproduction number, denoted as R S E . Estimation of parameter values is done by fitting the model to real tuberculosis data reported by the World Health Organization for Tanzania, covering the years 2000 to 2023. The system of equations is solved using the Predict-Evaluate-Correct-Evaluate Adams–Bashforth–Moulton scheme. Both analytical and numerical results indicate that increasing funding for vaccination programs, raising the level of disease-induced fear, and higher proportion of patients with positive attitudes towards hospital-based treatment can potentially reduce the disease burden in the community. Furthermore, incorporating human behavioral responses and experiences improves the accuracy of future disease dynamics predictions rather than ignoring them.