Power spectral density and similarity analysis of COVID-19 mortality waves across countries

Abstract

Background: During the COVID-19 pandemic, the Johns Hopkins University Center for Systems Science and Engineering (CSSE) established a comprehensive database detailing daily mortality rates across countries. This dataset revealed fluctuating global mortality trends attributable to COVID-19; however, the specific differences and similarities in mortality patterns between countries remain insufficiently explored. Consequently, this study employs Fourier and similarity analyses to examine these patterns within the frequency domain, thereby offering novel insights into the dynamics of COVID-19 mortality waves across different nations.

Methods: We employed the Fast Fourier transform to calculate the power spectral density (PSD) of COVID-19 mortality waves in 199 countries from January 22, 2020, to March 9, 2023. Moreover, we performed a cosine similarity analysis of these PSD patterns among all the countries.

Results: We identified two dominant peaks in the grand averaged PSD: one at a frequency of 1.15 waves per year (i.e., one wave every 10.4 months) and another at 2.7 waves per year (i.e., one wave every 4.4 months). We also found a cosine similarity index distribution with a skewness of -0.54 and a global median of cosine similarity index of 0.84, thus revealing a remarkable similarity in the dominant peaks of the COVID-19 mortality waves.

Conclusion: These findings could be helpful for planetary health if a future pandemic of a similar scale occurs so that effective confinement measures or other actions could be planned during these two identified periods.

Power spectral density (PSD) of worldwide COVID-19 mortality waves. The image of Earth was sourced from Pixabay, which offers free images.

Fig. 1

Examples of COVID-19 mortality waves and their power spectral density (PSD). A. Examples of time series showing a high number of COVID-19 deaths per day from eight countries. B. Normalized PSD is calculated from the time series shown in the left panel. Note that these countries exhibit a dominant peak around a frequency of one peak per year.

Fig. 2

Global COVID-19 mortality waves worldwide. The purple trace is the grand average of the power spectral density (PSD) obtained from the COVID-19 mortality time series for 199 countries. The traces in grey color represent the standard deviation. Note the two dominant COVID-19 mortality waves occurring at frequencies of 1.15 waves/year (i.e., one wave every 10.4 months) and 2.7 waves/year (i.e., one wave every 4.4 months). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3

A cosine similarity matrix for COVID-19 mortality was obtained by comparing all pairs of power spectral density (PSD) graphs for 199 countries listed in Table 1. The right vertical bar represents the cosine similarity index scale from 0 to 1. The numbers on the horizontal and vertical axes of this matrix represent the countries listed in alphabetical order in Table 1. Matrix regions shaded towards yellow indicate pairs of countries with high PSD similarity, while regions shaded towards green indicate low similarity.

Fig. 4

The histogram of the cosine similarity indexes was obtained from the cosine similarity index matrix shown in Fig. 3. This histogram shows a negatively skewed distribution of the cosine similarity indexes for 199 countries with a skewness of −0.54. The formula Th = Mean-Std was used to calculate the threshold “Th” to separate a data group with low cosine similarity (green parenthesis) and a data group with high cosine similarity (yellow parenthesis). Std is for standard deviation. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 5

It has the same format as Fig. 1 but for eight countries with a cosine similarity index below the threshold = mean-std = 0.71. A. Examples of time series showing a relatively low number of COVID-19 deaths per day from eight countries. B. Normalized power spectral density (PSD) is calculated from the time series shown in the left panel. These countries exhibit a multi-peak behavior in their PSD, occurring at different frequencies.

Fig. 6

It has the same format as Fig. 2, but the grand average of the power spectral density (PSD) was obtained from 17 countries that exhibited a similarity index below 0.71. Note a multipeak behavior in the COVID-19 mortality waves occurring at different frequencies from 0.4 to 4.7 COVID-19 mortality waves per year.

Fig. 7

It has the same format as Fig. 2 but for n = 182 countries with a cosine similarity index above the threshold = mean-std = 0.71. The averaged power spectral density (PSD) for these 182 countries still exhibits two dominant peaks at similar frequencies of 1.03 and 2.62 peaks per year, as the grand averaged PSD for 199 countries.