融合物理信息神经网络的呼吸道流行传染病传播动力学建模与分析

Modeling and Analysis of Respiratory Epidemic Transmission Dynamics Using Physics-Informed Neural Networks

摘要: 呼吸道流行传染病的传播过程受到人口流动、社会接触模式和防控措施等多方面的影响。基于传染病动力学模型在观测数据有限的情况下，难以准确刻画疫情的传播机制。为此，本文构建了一种融合物理信息神经网络和传染病动力学模型的分析框架DNN-PINN-SIR，通过将传染病传播机理以微分方程残差形式嵌入神经网络训练过程，在有限的观测数据下，可靠地辨识了疫情的传播动态并精准识别时变传播参数。在南京市2021年呼吸道传染病区域性暴发的实证分析中，所提出的DNN-PINN-SIR模型较常参数SIR模型在拟合精度与动力学解释能力方面均表现出更优性能，能够揭示传播率、有效再生数等核心指标的阶段性演化规律，为传染病传播动力学的定量分析与防控措施效果评估提供了一种新的建模思路。

Abstract: Respiratory epidemic transmission is shaped by multiple factors, including population mobility, social contact patterns, and intervention measures. However, when observational data are limited, conventional infectious-disease dynamical models often struggle to accurately capture the underlying transmission mechanisms. To address this issue, this paper develops an integrated framework, DNN-PINN-SIR, that combines physics-informed neural networks with infectious-disease dynamics. By embedding the transmission mechanism into the neural network training process in the form of differential-equation residuals, the proposed approach can reliably reconstruct transmission dynamics and accurately identify time-varying transmission parameters from sparse observations. In an empirical analysis of a regional respiratory infectious-disease outbreak in Nanjing in 2021, the proposed DNN-PINN-SIR model outperforms the constant-parameter SIR model in both fitting accuracy and dynamical interpretability, revealing the stage-wise evolution of key indicators such as the transmission rate and the effective reproduction number. This work provides a new modeling approach for quantitative analysis of infectious disease transmission dynamics and for evaluating the effectiveness of intervention measures.