Evaluating the impact of vaccination and progression delays on tuberculosis dynamics with disability outcomes: A case study in Saudi Arabia

Tuberculosis (TB) remains a major global health concern due to its infectious nature and complex treatment process. In this study, we developed a mathematical model incorporating TB progression, vaccination, latency delays, and disability outcomes. The compartmental model includes seven stages: Susceptible, vaccinated, latent, infectious, quarantined, recovered, and disabled, with time-delay terms capturing disease progression dynamics. The stability analysis of the equilibria was performed, and the sensitivity analysis was conducted using the direct differentiation method. The basic reproduction number $R_0$ was derived to assess TB spread under different interventions. Model parameters were estimated using Ordinary Least Squares (OLS) based on Saudi Arabia's TB data (2000–2023). Numerical simulations, solved via the Adams-Bashforth-Moulton method, highlight the impact of delayed latency and quarantine on TB control, emphasizing the need for timely interventions.