Adaptive Fourier decomposition-based time-frequency analysis of COVID-19 epidemic trends and policy interventions in Washington D.C., with comparative validation in London.

Background: Epidemic trends respond dynamically to public health interventions, and retrospective evaluation of these responses is important for future preparedness. However, conventional epidemiological and time-series approaches often have limited ability to resolve the multi-scale and non-stationary fluctuations of epidemic data, which may obscure temporal structures associated with intervention timing. This study aimed to apply adaptive Fourier decomposition (AFD) to characterize coronavirus disease 2019 (COVID-19) epidemic dynamics and examine their temporal associations with public health policy interventions. Methods: Daily confirmed COVID-19 case data for Washington D.C. were collected through a multi-step source verification process using public data repositories and official local surveillance records. The archived New York Times COVID-19 GitHub repository was used as the initial structured dataset, and the Washington D.C. case series was cross-checked and corrected against the official District of Columbia government COVID-19 surveillance data. Public health intervention data were collected primarily from official mayoral orders and related policy announcements issued by the District of Columbia government. The epidemic time series and policy timeline were then aligned chronologically, and the Washington D.C. study period was divided into five epidemic waves. For comparative validation, the London daily COVID-19 case series was obtained from the authors of a published AFD-based study. AFD was applied to decompose the epidemic time series into interpretable time-frequency components, and newly constructed components were further generated for correlation analysis. The decomposition results were compared with those obtained using empirical mode decomposition (EMD) and variational mode decomposition (VMD). Results: The third-order AFD components showed the strongest correlations with the original epidemic signal and effectively captured both long-term trend variation and short-term local fluctuations. In Washington D.C., the third-order components performed particularly well during the Omicron-dominated fifth wave, when major policy adjustments were implemented. Compared with EMD and VMD, AFD provided clearer multi-scale structures and stronger statistical associations with observed epidemic trajectories. Similar decomposition patterns and correlation results were observed in the London comparison, supporting the robustness of the proposed framework in a comparative urban setting. Conclusions: AFD provides a useful framework for analyzing non-stationary epidemic time series and for retrospectively examining temporal relationships between epidemic waves and public health interventions. In this study, the low-frequency and third-order AFD components captured the major epidemic trend more effectively than the comparison methods, suggesting that AFD may help identify meaningful shifts in epidemic structure under changing intervention conditions. These findings indicate that AFD may complement conventional epidemic surveillance by supporting interpretation of multi-scale epidemic fluctuations, improving assessment of intervention timing, and providing an additional analytical reference for future mitigation planning and monitoring of respiratory infectious disease outbreaks.