A mathematical model of TB transmission dynamics incorporating delays in funding and treatment programs

Tuberculosis (TB) remains a persistent global health concern, particularly in high-burden countries where delays in funding allocation and treatment initiation hinder control efforts. In this study, we introduced a delay-differential TB transmission model that incorporated two critical delays: The funding response delay ($ \tau_1 $) and the treatment initiation delay ($ \tau_2 $). The model was calibrated using South African TB incidence data from 2000–2023 to assess how these delays influence disease dynamics and system stability. Analytical results revealed that short delays lead the system toward a stable endemic equilibrium, while exceeding critical thresholds triggers a Hopf bifurcation, resulting in oscillatory or recurrent outbreaks. The treatment delay ($ \tau_2 $) exhibited a stronger destabilizing impact than the funding delay ($ \tau_1 $), underscoring the importance of timely diagnosis and treatment initiation in maintaining control. Sensitivity analysis identified prevention efficiency ($ \alpha $), treatment rate ($ \gamma $), and funding responsiveness ($ \omega $) as key parameters in suppressing transmission, whereas prolonged delays and higher depletion rates of prevention and funding programs elevated disease prevalence. From a policy perspective, the findings highlight that administrative bottlenecks and slow institutional responses can unintentionally amplify TB transmission, even under strong intervention programs. Maintaining steady funding flows, improving program responsiveness, and minimizing diagnostic delays are therefore essential for sustainable TB reduction. Overall, the proposed model offers a comprehensive framework for understanding how time delays influence TB dynamics and provides practical insights to guide responsive, data-driven strategies for effective TB control and elimination.