论文标题
COVID-19的扩展中的缩放特征
Scaling features in the spreading of COVID-19
论文作者
论文摘要
自COVID-19爆发以来，已经进行了许多数据分析。其中一些是基于假定指数增长的经典流行病学方法，但是一些研究报告说，幂律缩放可能可以更好地适合当前可用的数据。在此，我们检查了中国的数据（01/20/2020---02/24/2020），并实际上发现增长在一个显着较远的时间段内遵循了幂律动力学。这些指数分别为$ 2.48（20）$，$ 2.21（6）$和$ 4.26（12）$，分别为确认的感染，死亡和治愈病例，表明大流行中的基本小世界网络结构。尽管对于死亡人数和治愈病例的数量，尚无明显的与幂律增长的偏差，但感染的数量显然出现了负偏差，特别是对于荷叶州以外的地区。这表明，由于巨大的遏制工作，病毒扩散的放缓开始。同时，我们发现，尽管大小的差异巨大，但感染数量的生长动力学对于湖北省和湖北以外地区表现出了很多相似之处。在此基础上，在日志图中，我们重新汇总了湖北以外地区的感染数量，使其与中国的总感染数量尽可能多地重叠，从中大概的外推就会产生2020年3月3日左右的大流行，感染的数量约为83,000美元。此外，通过以日志量表分析死亡率的动力学，我们获得了一个粗略的估计，即3月3日，Covid-19的死亡率约为$ 4.7 \％\％\％\厚度5.0 \％5.0 \％\％$ $ $ 0.7 \％\％\％\％\％\％\％\％\ themsim1.0 \％。我们强调，由于数据分析纯粹是经验的，并且使用了各种假设，因此我们的预测可能是不可靠的。
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.
