媒体宣传干预下肺结核–流感混合传播动力学模型构建与分析

Establishment and Analysis of a Tuberculosis-Influenza Co-Transmission Dynamical Model under Media Publicity Intervention

摘要: 肺结核与流感的混合传播引发双病叠加流行，对人类健康与公共卫生安全构成重大威胁。针对该问题，本文构建了一类考虑媒体宣传干预的新型SEIICCR传染病动力学模型。通过严格的理论分析，证明了在任意非负初始条件下，模型所有状态变量的解均满足非负性与有界性，确保了模型的生物学合理性；采用下一代矩阵法求解模型的基本再生数R₀，并推导得出当R₀ < 1时系统存在唯一无病平衡点E₀，结合Routh-Hurwitz准则与构造的合适Lyapunov函数，严格证实了无病平衡点E₀的局部渐近稳定性与全局渐近稳定性。通过数值模拟验证了理论分析的有效性，并量化揭示了关键参数对R₀的影响。最后，基于新疆维吾尔自治区近年病例数据开展实证分析，研究结果为该区域内肺结核与流感的联合防控提供了科学依据与实践参考。

Abstract: The co-transmission of tuberculosis and influenza has led to a superimposed dual epidemic, posing a significant threat to human health and public health security. To address this issue, this paper constructs a novel SEIICCR dynamic model of infectious diseases that incorporates media publicity intervention. Through rigorous theoretical analysis, it is proved that the solutions of all state variables in the model are non-negative and bounded under any non-negative initial conditions, which ensures the biological rationality of the model. The basic reproduction number R₀ of the model is derived using the next-generation matrix method, and it is shown that the system has a unique disease-free equilibrium E₀ when R₀ < 1. Combined with the Routh-Hurwitz criterion and an appropriately constructed Lyapunov function, the local asymptotic stability and global asymptotic stability of E₀ are rigorously verified. Numerical simulations are conducted to validate the effectiveness of the theoretical analysis and quantitatively reveal the influence of key parameters on R₀. Finally, an empirical analysis is carried out based on recent case data from the Xinjiang Uygur Autonomous Region. The results provide scientific and feasible decision-making references for the prevention and control of the dual epidemic of tuberculosis and influenza in the region.