[论文解读] Scaling features in the spreading of COVID-19

Ming Li, Jie Chen+1 more|arXiv (Cornell University)|Feb 21, 2020

COVID-19 epidemiological studies参考文献 10被引用 31

一句话总结

本文分析中国早期新冠疫情数据（01/20/2020–02/24/2020）在对数-对数坐标下，发现感染、死亡、治愈呈幂律增长，具有不同的分形指数，暗示小世界网络影响，并提供对疫情峰值与死亡率的初步预测。

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 $4.7\% hicksim 5.0\%$ for Hubei province and $0.7\% hicksim1.0\%$ 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.

研究动机与目标

• 评估在初期暴发期间，中国的 COVID-19 增长是否遵循幂律增长而非指数增长。
• 从累积数据中识别感染、治愈与死亡的分形（尺度）指数。
• 探索区域特异性动态（湖北 vs. 湖北以外地区）并评估封控对增长趋势的影响。
• 基于对数-对数数据坍缩提供对疫情峰值与死亡率的初步外推。

提出的方法

• 分析中国大陆在 01/20/2020 到 02/24/2020 的感染、治愈及死亡累积计数。
• 在对数-对数尺度绘制数据以拟合幂律动力学并提取分形指数（α_infec、α_death、α_cured）。
• 在对数-对数平面使用重新缩放和多项式拟合，在无新的疫情爆发假设下估计疫情最大值和结束日。
• 比较湖北与湖北以外地区的增长动力学，以推断共同的传播机制和网络结构。

实验结果

研究问题

• RQ1 累积的 COVID-19 数据是否在较长时间范围内呈幂律增长？相应的分形指数是多少？
• RQ2 感染、死亡和治愈案例的估计指数是多少，它们对潜在网络有何含义？
• RQ3 对湖北以外地区数据的重新缩放是否可以预测中国整体的疫情峰值及时间？
• RQ4 湖北与中国其他地区的增长模式有何差异？这对封控影响有何启示？
• RQ5 能从对数-对数分析和外推中推断出哪些初步死亡率？

主要发现

• 感染、死亡和治愈呈幂律增长，分形指数约为 α_infec ≈ 2.5，α_death ≈ 2.2，α_cured ≈ 4.3。
• 在 02/12/2020 之后，感染出现负偏差，特别是在湖北以外地区，表明因封控而减缓传播。
• 治愈比率的指数远大于感染/死亡的指数，提示医疗网络连通性更密集。
• 将湖北以外地区的感染重新缩放以与中国总感染重叠，暗示在 2020 年 3 月 3 日（±2 天）附近，感染峰值约为 83,000（≈83,200）。
• 在外推下，总感染和治愈/死亡的结束日大致落在 2020/03/07 至 2020/03/19 之间。
• 在 2020/03/03 左右的初步死亡率外推结果为：湖北约 4.7%–5.0%、湖北以外地区约 0.8%–1.0%、中国整体约 4.0%–4.5%。