一类具有早期筛查和疫苗接种等多种控制措施的百日咳传播模型的动力学分析
Dynamical Analysis of a Pertussis Transmission Model with Multiple Control Measures Incorporating Early Screening and Vaccination
DOI: 10.12677/aam.2025.149402, PDF,    科研立项经费支持
作者: 刘 堃, 王晓静*：北京建筑大学理学院，北京
关键词: 百日咳；稳定性；疫苗接种；早期筛查；隔离；Pertussis； Stability； Vaccination； Early Screening； Isolation
摘要: 基于百日咳的传播动力学特性，本文建立了一类包含早期筛查和疫苗接种等多种控制措施的SEVIQR百日咳传播模型。通过理论分析，我们证明了当控制再生数小于1时，系统的无病平衡点具有全局渐近稳定性；当控制再生数大于1时，系统存在唯一的地方病平衡点。进而，通过敏感性分析揭示了各控制参数对疾病传播的影响程度。数值模拟结果表明：提高疫苗接种覆盖率、加强早期筛查频率以及强化隔离措施等综合干预策略能显著遏制百日咳的传播。
Abstract: Based on the transmission dynamics of pertussis, a SEVIQR pertussis transmission model with multiple control measures incorporating early screening and vaccination is constructed. Through theoretical analysis, we rigorously prove that when the control reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable, whereas when the control reproduction number is more than one, the system admits a unique endemic equilibrium. Furthermore, sensitivity analysis is conducted to evaluate the impact of control parameters on disease transmission. Numerical simulations demonstrate that comprehensive intervention strategies including increasing vaccination coverage, enhancing early screening frequency and strengthening isolation measures can significantly suppress the transmission of pertussis.
文章引用：刘堃, 王晓静. 一类具有早期筛查和疫苗接种等多种控制措施的百日咳传播模型的动力学分析[J]. 应用数学进展, 2025, 14(9): 88-99. https://doi.org/10.12677/aam.2025.149402

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