基于双线性发生率的耐药结核病模型的动力学分析

Dynamic Analysis of a Multidrug-Resistant Tuberculosis Model Based on Bilinear Incidence Rates

摘要: 本研究在七个仓室耐药结核病动力学模型基础上，将标准发生率改为双线性发生率，并对其动力学性质进行了深入分析。通过构造Lyapunov函数和利用Routh-Hurwitz判据，我们证明了当基本再生数R₀ < 1时，系统的无病平衡点是全局渐近稳定的；当R₀ > 1，系统存在唯一的地方病平衡点。进一步地，我们结合世界卫生组织(WHO)的公开数据对模型参数进行了重新拟合。数值模拟结果说明降低传播率和加强潜伏染病者干预是目前最有效的防控策略；通过综合干预措施中国有望在2035年实现终结结核病的目标。本研究为耐药结核病防控策略的制定提供了理论依据和量化评估工具。

Abstract: This study replaces the standard incidence rate with a bilinear incidence rate in a seven-compartment drug-resistant tuberculosis (DR-TB) dynamics model and analyze its dynamic properties. By constructing a Lyapunov function and applying the Routh-Hurwitz criterion, we demonstrate that when the basic reproduction number R₀ < 1, the disease-free equilibrium point is globally asymptotically stable. When R₀ > 1, the system possesses a unique endemic equilibrium point. Furthermore, model parameters were refitted using publicly available data from the World Health Organization (WHO). Numerical simulations not only validated the theoretical analysis but also indicated that China could achieve the goal of ending tuberculosis by 2035 through comprehensive intervention measures. This study provides a theoretical foundation and quantitative assessment tools for formulating drug-resistant tuberculosis control strategies.