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⟩≈0.87 for Germany; ⟨ r⟩≈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 ξ=152±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 mR is uncorrelated with local~r (null result), the national (mR,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.
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BibTeX
@misc{bernalalvarado2026kuramoto,
title = {{Kuramoto Phase Synchronization in Regional Epidemic Dynamics: Two Test Cases from European COVID-19 and Influenza Surveillance}},
author = {Jose de Jesus Bernal-Alvarado and David Delepine},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06899},
eprint = {2609.06899},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06899},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Kuramoto Phase Synchronization in Regional Epidemic Dynamics: Two Test Cases from European COVID-19 and Influenza Surveillance
AU - Jose de Jesus Bernal-Alvarado
AU - David Delepine
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.06899
UR - https://arxiv.org/abs/2609.06899
AB - 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⟩≈0.87 for Germany; ⟨ r⟩≈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 ξ=152±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.
ER -