AI 中文总结
研究SEIR模型参数难测及估计问题，通过观测系统方法对其进行重新参数化，实现全局可识别与计算稳定，消除非唯一性，经实验验证新方法能提高收敛频率、避免错误，纳入灵敏度方程增强鲁棒性和速度，为传染病预测等提供可靠见解。
AI 中文摘要
易感-暴露-感染-康复（SEIR）模型是流行病学中的基本模型。诸如传播、潜伏期和感染率等模型参数通常难以直接测量，需通过求解优化问题来估计。然而，标准SEIR系统参数并非全局可识别，导致优化算法常收敛到错误的局部最优且存在数值刚性。本文对SEIR框架进行综合结构可识别性分析，通过观测系统方法给出全局可识别且计算稳定的模型重新参数化。刻画了多个局部可识别参数，消除参数估计中的非唯一性问题。数值实验表明新公式显著提高收敛频率，避免数值溢出导致的运行时错误，能一致恢复正确参数。将一阶灵敏度方程纳入优化器可增强估计过程的鲁棒性和执行速度。数值条件良好的参数识别方法及对参数可识别性的全面理解，确保模型为传染病预测和理论流行病学提供可靠、严谨的见解。
英文摘要
The Susceptible-Exposed-Infectious-Removed (SEIR) model is a fundamental model in epidemiology. Model parameters such as the reciprocal transmission, incubation, and infectious rates are often difficult to measure directly, and they are estimated by solving an optimisation problem aiming to minimise the difference between the observed data and the model solution. However, the parameters of the standard SEIR system are not globally identifiable, causing optimisation algorithms to frequently converge to incorrect local optima and suffer from numerical stiffness. Here we show a comprehensive structural identifiability analysis of the SEIR framework, and present a globally identifiable and computationally stable reparameterisation of the model derived via an observational system approach. We fully characterise the multiple locally identifiable parameters, and by transforming the system into a globally identifiable structure, we eliminate the non-uniqueness issues in the parameter estimation approaches. Our numerical experiments demonstrate that this reformulation significantly improves convergence frequency, avoids runtime errors caused by numerical overflow, and consistently recovers the correct parameters. Furthermore, incorporating first-order sensitivity equations into the optimiser enhances the robustness and execution speed of the estimation process. Numerically well-conditioned methods for parameter identification, together with a comprehensive understanding of the identifiability of the parameters, ensure that the model yields reliable, rigorous insights for infectious disease forecasting and theoretical epidemiology.
