Dynamic and optimal control of TB transmission: the role of vaccination funding and social processes using Caputo-type framework

This study highlights the significance of vaccination funding and social-based control strategies on management of tuberculosis. To effectively account for human experiences, the 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, Banach contraction mapping and the Ulam–Hyers approach. The system of equations is solved using the predict–evaluate–correct–evaluate Adams–Bashforth–Moulton scheme. The next-generation matrix technique is adopted to derive the socioeconomic control reproduction number RC. Estimation of parameter values for the uncontrolled model is done by fitting the model to real tuberculosis data reported by the World Health Organization for Tanzania, covering the years 2000 to 2023. Both analytical and numerical results indicate that implementation of control strategies related to increased vaccination funding, enhanced TB-induced fear and higher proportion of patients with positive attitudes toward hospital-based treatment can effectively suppress the burden of tuberculosis within the community. Furthermore, the cost-effectiveness analysis shows that the optimal control strategy targeting TB-induced fear is the most efficient and cost-effective option for controlling the disease among the strategies considered.