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. 2022 Apr;185(2):699-719.
doi: 10.1111/rssa.12800. Epub 2022 Mar 11.

Power law in COVID-19 cases in China

Affiliations

Power law in COVID-19 cases in China

Behzod B Ahundjanov et al. J R Stat Soc Ser A Stat Soc. 2022 Apr.

Abstract

The novel coronavirus (COVID-19) was first identified in China in December 2019. Within a short period of time, the infectious disease has spread far and wide. This study focuses on the distribution of COVID-19 confirmed cases in China-the original epicentre of the outbreak. We show that the upper tail of COVID-19 cases in Chinese cities is well described by a power law distribution, with exponent around one in the early phases of the outbreak (when the number of cases was growing rapidly) and less than one thereafter. This finding is significant because it implies that (i) COVID-19 cases in China is heavy tailed and disperse; (ii) a few cities account for a disproportionate share of COVID-19 cases; and (iii) the distribution generally has no finite mean or variance. We find that a proportionate random growth model predicated by Gibrat's law offers a plausible explanation for the emergence of a power law in the distribution of COVID-19 cases in Chinese cities in the early phases of the outbreak.

Keywords: COVID‐19; Gibrat's law; Pareto distribution; coronavirus; heavy tailedness; power law; proportionate random growth.

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Figures

FIGURE 1
FIGURE 1
Chinese cities with confirmed COVID‐19 cases as of May 23, 2020 Data source: Harvard Dataverse (China Data Lab, 2020) [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 2
FIGURE 2
The number of Chinese cities with confirmed COVID‐19 cases over time Data source: Harvard Dataverse (China Data Lab, 2020)
FIGURE 3
FIGURE 3
The empirical distribution of cumulative number of COVID‐19 confirmed cases for Chinese cities. The empirical distribution is obtained using kernel density with Epanechnikov kernel and the smoothing bandwidth based on unbiased cross‐validation method [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 4
FIGURE 4
The ratio of COVID‐19 cases to city population in China between 15 January 2020 and 23 May 2020 [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 5
FIGURE 5
Plot of empirical and fitted log counter‐cumulative probability and log COVID‐19 confirmed cases. Estimation is based on upper‐tail observations x>xmin as of 23 May 2020, where xmin is determined based on the minimization of the KS statistic [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 6
FIGURE 6
Sensitivity analysis with the choice of xmin. Estimation for each given choice of xmin is based on upper‐tail observations x>xmin as of 23 May 2020. The vertical (dashed) line indicates the position of optimal (data‐driven) choice xmin. For the Gabaix and Ibragimov (2011) test, the null hypothesis that COVID‐19 confirmed cases is distributed according to a power law is rejected if a goodness‐of‐fit statistic is greater than a corresponding threshold value [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 7
FIGURE 7
Power law analysis over the first wave of the pandemic. Estimation is based on upper‐tail observations x>xmin on each day, where xmin for each date is determined based on the minimization of the KS statistic. For the Gabaix and Ibragimov (2011) test, the null hypothesis that COVID‐19 confirmed cases is distributed according to a power law is rejected if a goodness‐of‐fit statistic is greater than a corresponding threshold value [Colour figure can be viewed at wileyonlinelibrary.com]
FIGURE 8
FIGURE 8
Estimates of ρt in Equation (22) between 23 January 2020 and 2 February 2020, with 95% confidence bands. ρt1 provides empirical evidence for Gibrat's law
FIGURE 9
FIGURE 9
Estimates of β0t, β1t, β2t, β3t in Equation (23) between 23 January 2020 and 2 February 2020, with 95% confidence bands. The parameters of interest are β1t, β2t, β3t, with β1t0, β2t0, β3t0 providing empirical evidence for Gibrat's law

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References

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