分年龄组传染病动力学的时变传染率优化模型与计算

Time-Varying Transmission Rate Optimization Model and Computation for Age-Structured Infectious Disease Dynamics

摘要: 传染病传播过程通常同时受到季节变化与人群异质性的共同影响，经典常系数、均质混合假设在刻画实际传播动力学时往往存在局限。针对这一问题，本文在考虑年龄结构差异的基础上，构建了一类分年龄组的变系数传染病动力学模型，并基于住院监测数据对各年龄组的时变传染率进行推断计算。数值算例结果表明，基于本文模型推断的传染率能够较好地反映流感季内传播强度的季节性变化特征，并揭示了不同年龄人群在传播水平与时间演化上的显著差异。模型对各年龄组住院人数的预测与观测数据在峰值位置、峰值规模及累计水平上均保持良好一致。本文所提出的模型在保证参数稳定性与模型可解释性的同时，有效刻画了年龄异质性与时变传播特征，可为流感等季节性传染病的传播机制分析、住院负担评估及后续干预策略研究提供定量参考。

Abstract: The transmission process of infectious diseases is usually influenced jointly by seasonal variation and population heterogeneity, and classical assumptions of constant coefficients and homogeneous mixing often have limitations in describing real transmission dynamics. To address this issue, this paper constructs a class of age-structured infectious disease dynamic models with variable coefficients by incorporating age-specific differences, and infers the time-varying transmission rates of each age group based on hospitalization surveillance data. Numerical examples show that the transmission rates inferred from the proposed model can well reflect the seasonal variation of transmission intensity during the influenza season, and reveal significant differences in transmission levels and temporal evolution among different age groups. The model predictions of hospitalizations for each age group remain in good agreement with the observed data in terms of peak timing, peak magnitude, and cumulative levels. The model proposed in this paper effectively characterizes age heterogeneity and time-varying transmission features while ensuring parameter stability and model interpretability, and can provide quantitative references for the analysis of transmission mechanisms, hospitalization burden assessment, and subsequent intervention strategy studies of seasonal infectious diseases such as influenza.