Scaling features in the spreading of COVID-19

TL;DR

This study analyzes COVID-19 data from China, revealing power-law growth patterns and suggesting a potential slowdown in virus spread, with approximate predictions for peak infection numbers and death rates based on empirical data.

Contribution

The paper demonstrates that COVID-19 growth follows power-law kinetics and provides empirical estimates for peak infection and death rates, highlighting network structure implications.

Findings

Power-law growth observed in infection, death, and cured cases.

Indications of slowing virus spread due to containment efforts.

Estimated peak infection around March 3, 2020, with specific death rates.

Abstract

Since the outbreak of COVID-19, many data analyses have been done. Some of them are based on the classical epidemiological approach that assumes an exponential growth, but a few studies report that a power-law scaling may provide a better fit to the currently available data. Hereby, we examine the data in China (01/20/2020--02/24/2020), and indeed find that the growth closely follows a power-law kinetics over a significantly wide time period. The exponents are $2.48(20)$, $2.21(6)$ and $4.26(12)$ for the number of confirmed infections, deaths and cured cases, respectively, indicating an underlying small-world network structure in the pandemic. While no obvious deviations from the power-law growth can be seen yet for the number of deaths and cured cases, negative deviations have clearly appeared in the number of infections, particularly that for the region outside Hubei. This suggests the beginning of the slowing-down of the virus spreading due to the huge containment effort. Meanwhile, we find that despite the dramatic difference in magnitudes, the growth kinetics of the infection number exhibits much similarity for Hubei province and the region outside Hubei. On this basis, in log-log plot, we rescale the infection number for the region outside Hubei such that it overlaps as much as possible with the total infection number in China, from which an approximate extrapolation yields the maximum of the pandemic around March 3, 2020, with the number of infections about $83,000$. Further, by analyzing the kinetics of the mortality in log-log scale, we obtains a rough estimate that near March 3, the death rate of COVID-19 would be about $4.7\%\thicksim 5.0\%$ for Hubei province and $0.7\%\thicksim1.0\%$ for the region outside Hubei. We emphasize that our predictions may be quantitatively unreliable, since the data analysis is purely empirical and various assumptions are used.