A tuberculosis model incorporating latent stratification and waning immunity with empirical analysis

Abstract

Based on the complex transmission mechanism of tuberculosis, this study constructs a novel class of infectious disease dynamical models incorporating low-risk latent infection, high-risk latent infection, and waning immunity after recovery. The basic reproduction number is rigorously derived using the next-generation matrix method, and the global asymptotic stability of both the disease-free equilibrium and the endemic equilibrium is mathematically proved under specific threshold conditions. Extensive numerical simulations are conducted to verify the theoretical results and illustrate the dynamic behavior of the proposed system. Furthermore, based on the empirical data of newly reported tuberculosis cases in China from 2005 to 2024, the Markov chain Monte Carlo method is employed to accurately estimate the unknown model parameters and predict the future transmission trend of the disease. The results of the partial rank correlation coefficient analysis indicate that the transmission rate and recovery rate are the most critical factors affecting tuberculosis dynamics. These findings provide robust theoretical support and quantitative insights for optimizing public health strategies and improving tuberculosis prevention and control measures. Additionally, the proposed mathematical framework highlights the importance of distinguishing between different latent infection risks, which can significantly enhance the precision of epidemiological forecasting and resource allocation in endemic regions worldwide. Ultimately, this research offers a comprehensive analytical tool for policymakers to design targeted interventions and mitigate the long-term burden of tuberculosis effectively.