区域流行病动态中的Kuramoto相位同步：来自欧洲COVID-19和流感监测的两个测试案例
Kuramoto Phase Synchronization in Regional Epidemic Dynamics: Two Test Cases from European COVID-19 and Influenza Surveillance
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- Universidad de Guanajuato（瓜纳华托大学）
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中文总结 AI 辅助
本研究用德国和欧洲的流行病数据验证Kuramoto模型，发现区域同步由长程共模场和短程扩散耦合构成，并识别出爆炸性同步特征及局部驱动因素。
中文摘要 AI 辅助
我们测试了Kuramoto模型是否能定量描述区域流行病波中的空间同步，使用了德国400个县（Kreise）的每日COVID-19发病率（2021-2023年）和12个欧洲国家的每周ILI率（ECDC，2021-2026年）。带通滤波和希尔伯特变换相位提取产生了较高的全局序参量（德国⟨r⟩≈0.87；欧洲⟨r⟩≈0.97），但两者均由共模驱动因素主导，而非成对局部耦合。去除共模后揭示了真正的短程同步：德国残差局部序呈指数衰减，相关长度ξ=152±6公里，欧洲面板中相邻与非相邻对比显著（Mann-Whitney p=0.005）。我们将这种跨两种疾病和两个空间尺度的收敛模式解释为一种普遍的双尺度结构：长程共模场叠加在较短程扩散耦合之上。与伴随的规范介导Doi-Peliti框架的交叉验证表明，地区级有效筛选质量m_R与局部r不相关（零结果），国家（m_R，r）相图独立重现了先前报告的滞后环，成对相位滞后定量匹配分数阶微积分预测。频率-度相关性提供了爆炸性同步的结构特征；共享同一联邦州（Bundesland）的地区之间的过度同步暗示共享学校假期日历和州级政策是局部耦合驱动因素。
英文摘要
We test whether the Kuramoto model quantitatively describes spatial synchronization in regional epidemic waves, using daily COVID-19 incidence for 400 German \emph{Kreise} (2021--2023) and weekly ILI rates for 12 European countries (ECDC, 2021--2026). Bandpass filtering and Hilbert-transform phase extraction yield high global order parameters ($\langle r\rangle\approx0.87$ for Germany; $\langle r\rangle\approx0.97$ for Europe), yet both are dominated by a common-mode driver rather than pairwise local coupling. Removing the common mode reveals genuine short-range synchronization: an exponentially decaying residual local order with correlation length $ξ=152\pm6$~km in Germany, and a significant neighbor-vs.-non-neighbor contrast (Mann--Whitney $p=0.005$) in the European panel. We interpret this convergent pattern across two diseases and two spatial scales as a universal two-scale structure: a long-range common-mode field superimposed on shorter-range diffusive coupling. Cross-validation against a companion gauge-mediated Doi--Peliti framework shows that district-level effective screening mass $m_R$ is uncorrelated with local~$r$ (null result), the national $(m_R,r)$ phase portrait independently reproduces a previously reported hysteresis loop, and pairwise phase lags quantitatively match fractional-calculus predictions. A frequency--degree correlation provides the structural signature of explosive synchronization; excess synchronization between districts sharing the same \emph{Bundesland} implicates shared school-holiday calendars and state-level policy as local coupling drivers.
