Abstract
The COVID-19 is one of the worst pandemics in modern history. We applied principal component analysis (PCA) to the daily time series of the COVID-19 death cases and confirmed cases for the top 25 countries from April of 2020 to February of 2021. We calculated the eigenvalues and eigenvectors of the cross-correlation matrix of the changes in daily accumulated data over monthly time windows. The largest eigenvalue describes the overall evolution dynamics of the COVID-19 and indicates that evolution was faster in April of 2020 than in any other period. By using the first two PC coefficients, we can identify the group dynamics of the COVID-19 evolution. We observed groups under critical states in the loading plot and found that American and European countries are represented by strong clusters in the loading plot. The first PC plays an important role and the correlations (C1) between the normalized logarithmic changes in deaths or confirmed cases and the first PCs may be used as indicators of different phases of the COVID-19. By varying C1 over time, we identified different phases of the COVID-19 in the analyzed countries over the target time period.
Highlights
The COVID-19 is an ongoing pandemic caused by the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [1]
We identified the COVID-19 states of countries based on the changes in the correlations of each country contributing to PC1 between two monthly time windows such as ΔC1 = C1(T+1)−C1(T) where T is the time period
Our study finds that the largest eigenvalues of the correlation matrix in the monthly time frame can be used to observe the dynamics of COVID-19 across the world
Summary
The COVID-19 is an ongoing pandemic caused by the transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) [1]. Different models have been applied to the time series of COVID-19 confirmed, death and recovered cases to observe and predict the COVID dynamics in different countries [9,10,11,12,13,14,15,16,17,18]. Autoregressive model is applied on real world time series data to forecast the confirmed and recovered COVID-19 cases [11]. The time series model based on two-piece scale mixture normal distribution is used to predict the number of confirmed cases and death rate of COVID-19 in the world [20]. We apply PCA to the correlations for the changes of cumulative time series of COVID-19 death and confirmed cases between different countries and characterize the evolving correlation structures within countries. The group dynamics of the affected countries is observed over time using first two PC coefficients not done before
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