Stability Analysis of Tuberculosis Models Including High‐Risk and Low‐Risk Latent Classes

ABSTRACT

Tuberculosis remains a global health problem due to complicated factors such as drug resistance and latency. This study examines the stability of equilibrium states in a tuberculosis model that distinguishes between high‐risk and low‐risk latent groups, reflecting various transmission routes. Local stability is analyzed using the Routh–Hurwitz criterion and center manifold theory, whereas global stability is analyzed by applying Lyapunov functions and LaSalle's invariance principle. Numerical simulations confirm and complement the theoretical results by demonstrating convergence to equilibrium points for various parameter values. Sensitivity analysis shows that the transmission threshold is governed primarily by the progression from the low‐risk latent class and the treatment and diagnostic parameters. In contrast, the parameters associated with the high‐risk pathway and the reinfection have comparatively limited effects on both the transmission threshold and the endemic equilibrium levels. This work lays the foundation for more complex model analysis and contributes to a better understanding and insight into tuberculosis epidemiology.