Abstract
This paper proposes a cluster-based method to analyze the evolution of multivariate time series and applies this to the COVID-19 pandemic. On each day, we partition countries into clusters according to both their cases and death counts. The total number of clusters and individual countries’ cluster memberships are algorithmically determined. We study the change in both quantities over time, demonstrating a close similarity in the evolution of cases and deaths. The changing number of clusters of the case counts precedes that of the death counts by 32 days. On the other hand, there is an optimal offset of 16 days with respect to the greatest consistency between cluster groupings, determined by a new method of comparing affinity matrices. With this offset in mind, we identify anomalous countries in the progression from COVID-19 cases to deaths. This analysis can aid in highlighting the most and least significant public policies in minimizing a country’s COVID-19 mortality rate.
Highlights
Understanding the trajectories of COVID-19 cases and death counts assists governments in anticipating and responding to the impact of the pandemic
The first 30 days carry some triviality in the cluster structure, with few cases observed outside China, so it may be desirable to exclude them from the analysis
While the cluster consistency offset seeks to align the similarity of case and death counts among individual countries, the series evolution offset seeks to quantify the overall spread of the data as a function of time
Summary
Understanding the trajectories of COVID-19 cases and death counts assists governments in anticipating and responding to the impact of the pandemic. The timely identification of anomalous countries, both successful and unsuccessful, provides opportunities to determine effective response strategies. This analysis can be difficult as death counts naturally lag behind case counts. This paper builds on the extensive literature of multivariate time series analysis, developing a new mathematical method and a more extensive analysis of COVID-19 dynamics than previously performed. Existing methods of time series analysis include parametric models,[1] such as exponential[2] or power-law models,[3] and nonparametric methods, such as distance analysis,[4] distance correlation,[5,6,7] and network models.[8] Both parametric and nonparametric methods have been used to model COVID-19.9,10
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