Kuramoto Phase Synchronization in Regional Epidemic Dynamics: Two Test Cases from European COVID-19 and Influenza Surveillance

Abstract

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 ($⟨r⟩\approx 0.87$ for Germany; $⟨r⟩\approx 0.97$ 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 $\xi =152\pm 6$~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.

22 pages, 15 figures