After being cured of tuberculosis, individuals do not acquire lifelong immunity and may become reinfected. Based on this context, we propose an epidemiological model incorporating treatment and recurrent tuberculosis. By calculating the basic reproduction number Formula: see text using the next-generation matrix method, We decouple the transmission thresholds for fast-progressing and slow-progressing tuberculosis. Key findings: backward bifurcation where the disease may persist even when Formula: see text, and bistability where multiple endemic equilibria coexist when forward bifurcation occurs at Formula: see text under certain conditions. We confirm that exogenous reinfection parameter Formula: see text induces backward bifurcation, and rigorously prove the existence of a critical threshold Formula: see text for recurrent reinfection parameter Formula: see text, demonstrating that Formula: see text alone can trigger backward bifurcation. The model innovatively incorporates differentiated treatment mechanisms for both successfully treated and treatment-failure cases, better reflecting clinical reality. We employ Bayesian MCMC methods with Guangdong TB surveillance data to estimate parameter posterior distributions and conduct global PRCC analysis. Numerical simulations demonstrate that optimized treatment strategies can reduce TB mortality by 93.33% by 2035, however, reaching the 2050 goals requires integrated measures including latent infection screening. This study provides quantitative evidence for precision TB control strategies.
Gan et al. (Mon,) studied this question.