Department of Civil, Environmental and Architectural Engineering, University of Padova, via Marzolo 9, Padova, Italy.
Department of Environmental Sciences, Informatics and Statistics, Ca' Foscari University of Venice, Via Torino 155, Venezia Mestre, Italy.
PLoS Comput Biol. 2024 Sep 5;20(9):e1012387. doi: 10.1371/journal.pcbi.1012387. eCollection 2024 Sep.
Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to vary in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and the state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the Italian COVID-19 pandemic. Our results show that the split implementation of PINNs outperforms the joint approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%). Finally, we illustrate that the proposed PINN-method can also be adopted to produced short-term forecasts of the dynamics of an epidemic.
房室模型为分析暴发期间相关传播过程、进行短期预测或传播情景模拟以及评估疫苗接种活动的影响提供了简单有效的工具。然而，由于许多因素会导致传播动力学的快速变化，房室模型的校准并不简单。例如，个人意识、非药物干预措施的实施和新变体的出现可能会发生变化。因此，诸如传播率之类的模型参数注定会随时间变化，这使得它们的评估更加具有挑战性。在这里，我们建议使用基于物理的神经网络（PINN）来跟踪模型参数和状态变量的时间变化。由于 PINN 能够同时考虑数据（通常是不确定的）和系统的控制方程中的信息，因此它们在许多工程应用中引起了关注。PINN 识别未知模型参数的能力使其特别适合解决病态反问题，例如在流行病学模型应用中出现的问题。在这里，我们开发了一种用于实施 PINN 的简化分割方法，以根据 SIR 模型方程和传染病数据来估计传染病的状态变量和传播率的时间变化。主要思想是首先在流行病学数据上进行训练，然后在系统方程的残差上进行训练。该方法应用于五个合成测试案例和两个再现意大利 COVID-19 大流行头几个月情况的真实场景。结果表明，在准确性（高达一个数量级）和计算时间（加速 20％）方面，PINN 的分割实施优于联合方法。最后，我们说明所提出的 PINN 方法也可以用于进行传染病动力学的短期预测。
