Modeling tuberculosis transmission dynamics in Algeria: Effects of vaccination, exogenous reinfection, and endogenous reactivation

This paper developed a novel nonlinear Susceptible–Vaccinated–Exposed–Infectious–Treated–Recovered–Susceptible (SVEITRS) compartmental model to investigate the transmission dynamics of tuberculosis (TB) in Algeria over the period between 1990–2024, explicitly accounting for partial Bacillus Calmette-Guérin (BCG) vaccine efficacy, endogenous reactivation of latent infection, and exogenous reinfection. The basic reproduction number ${\mathcal{R}}_0$ was derived using the next-generation matrix approach, and rigorous analytical results were established for the local and global stability of both the disease-free and endemic equilibrium points. Model parameters were estimated by fitting the model to Algerian TB surveillance data, achieving a coefficient of determination of $R^2=0.84$, which indicates a strong agreement between the model predictions and reported epidemiological trends. A global sensitivity analysis based on partial rank correlation coefficients (PRCCs) reveals that demographic recruitment and transmission-related parameters exert the greatest influence on TB dynamics, whereas intervention-related parameters such as vaccination and treatment rates have a comparatively weaker impact. These findings indicate that vaccination alone is insufficient to eliminate TB and highlight the need for integrated control strategies that combine sustained vaccination coverage, early case detection, and effective management of latent infections. The proposed modeling framework provides a quantitative basis for evaluating TB control policies in high-burden settings such as Algeria.