Mathematical Modeling and Cost-Effective Control of Tuberculosis through Vaccination and Treatment

Abstract

Tuberculosis (TB) remains a major global health concern, particularly in high-burden countries such as Indonesia. To better understand the transmission dynamics and evaluate intervention strategies, a compartmental SVEITR model is developed that incorporates vaccination, exposure, treatment adherence, and immunity loss. Using next-generation matrix methods, the basic reproduction number is derived and stability analysis demonstrated that the disease-free equilibrium is globally asymptotically stable when . Bifurcation analysis of the vaccine efficacy parameter revealed a forward bifurcation, indicating that TB can be eradicated once vaccine efficacy exceeds a critical threshold. Using Pontryagin's maximum principle, we developed an optimal control problem with time-dependent vaccination and treatment adherence control. Numerical simulations demonstrated that the combined implementation of vaccination and treatment adherence resulted in the greatest reduction in the exposed and infectious population. Further cost-effectiveness analysis showed that improving treatment adherence alone was the most economically efficient strategy (ACER ; ICER ), while vaccination alone was significantly less cost-effective (ACER ). Although combining vaccination with treatment adherence achieved additional health benefits, it incurs higher additional costs (ICER). These findings suggest that treatment adherence should be prioritized in resource-limited settings, with combined strategies considered when additional resources are available.