Amplitude-Phase Analysis of the COVID-19 Point Process and the Early Countermeasures

2026-08-10

AI Summary

This study investigates how early government interventions influenced the transmission dynamics of the COVID-19 pandemic, with a focus on their regulatory effects on the amplitude and temporal phase of infection curves. By modeling daily case counts across U.S. states as point processes, the authors introduce a novel analytical framework that integrates nonparametric amplitude-phase decomposition with Wasserstein principal component analysis (PCA) to extract temporal features of epidemic trajectories. Using the Oxford Stringency Index as a covariate in a vector regression model, the approach innovatively incorporates amplitude-phase separation into point process analysis of epidemic data. The findings reveal that the timing of intervention significantly shapes infection curve morphology: early implementation is strongly associated with flatter epidemic curves, whereas overall stringency—or the cumulative “stringency budget”—shows no significant association with total case counts.

Abstract

We investigate how governmental restrictions relate to the spread and temporal dynamics of COVID-19 early in the pandemic. We model daily infection data from each US state as realisations of a point process, taking the random intensity measure to be the latent object of interest and, crucially, allowing these realisations to vary not only in magnitude but also in the temporal dynamics. By non-parametrically separating these amplitude and phase variations, we examine how government restrictions relate to each source of variability, relating the infection curves to the Oxford Stringency Index, which we treat as a measure on the same time window. Employing Wasserstein PCA, we analyse the temporal variability of both the infections and the restrictions. We then use the resulting scores, together with the scalars representing the overall stringency budget and the total infection count, as inputs to a linear vector-on-vector regression model. Our findings suggest that, when considering the separate contributions of amplitude and phase variability, earlier implementation of restrictions is associated with flatter infection curves. By contrast, we do not find significant evidence of an association between stringency and total infection counts, nor between the overall stringency budget and the infection outcomes considered.

Problem

• COVID-19
• government restrictions
• temporal dynamics
• amplitude-phase variability
• point process

Innovation

• point process
• amplitude-phase separation
• Wasserstein PCA
• Oxford Stringency Index
• temporal dynamics