AN EPIDEMIOLOGICAL MODEL INCORPORATING TREATMENT AND RECURRENT TUBERCULOSIS WITH BIFURCATION ANALYSIS AND PARAMETER ESTIMATION

After being cured of tuberculosis (TB), individuals do not acquire lifelong immunity and may become reinfected. Based on this context, we propose an epidemiological model incorporating treatment and recurrent TB. 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 TB. 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.