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新型冠状病毒肺炎早期时空传播特征分析

王聪 严洁 王旭 李敏

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新型冠状病毒肺炎早期时空传播特征分析

王聪, 严洁, 王旭, 李敏

Analysis on early spatiotemporal transmission characteristics of COVID-19

Wang Cong, Yan Jie, Wang Xu, Li Min
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  • 通过最新公布的流行病学数据估计了易感者-感染者模型参数, 结合百度迁徙数据和公开新闻报道, 刻画了疫情前期武汉市人口流动特征, 并代入提出的支持人口流动特征的时域差分方程模型进行动力学模拟, 得到一些推论: 1)未受干预时传染率在一般环境下以95%的置信度位于区间[0.2068, 0.2073], 拟合优度达到0.999; 对应地, 基本传染数R0位于区间[2.5510, 2.6555]; 极限环境个案推演的传染率极值为0.2862, 相应的R0极值为3.1465; 2)百度迁徙规模指数与铁路发送旅客人数的Pearson相关系数达到0.9108, 有理由作为人口流动的有效估计; 3)提出的模型可有效推演疫情蔓延至外省乃至全国的日期, 其中41.38%的预测误差 ≤ 1 d, 79.31%的预测误差 ≤ 3 d, 96.55%预测误差 ≤ 5 d, 总体平均误差约为 2.14 d.
    In this paper, a simple susceptible-infected (SI) model is build for simulating the early phase of COVID-19 transmission process. By using the data collected from the newest epidemiological investigation, the parameters of SI model is estimated and compared with those from some other studies. The population migration data during Spring festival in China are collected from Baidu.com and also extracted from different news sources, the migration characteristic of Wuhan city in the early phase of the epidemic situation is captured, and substituted into a simple difference equation model which is modified from the SI model for supporting migrations. Then several simulations are performed for the spatiotemporal transmission process of COVID-19 in China. Some conclusions are drawn from simulations and experiments below. 1) With 95% confidence, the infection rate of COVID-19 is estimated to be in a range of 0.2068–0.2073 in general situation, and the corresponding basic reproduction number R0 is estimated to be in a range of 2.5510–2.6555. A case study shows that under an extreme condition, the infection rate and R0 are estimated to be 0.2862 and 3.1465, respectively. 2) The Pearson correlation coefficient between Baidu migration index and the number of travelers sent by railway is 0.9108, which indicates a strong linear correlation between them, thus it can be deduced that Baidu migration index is an efficient tool for estimating the migration situation. 3) The epidemic arrival times for different provinces in China are estimated via simulations, specifically, no more than 1 day within an estimation error of 41.38%; no more than 3 days within an error of 79.31%, and no more than 5 days with an error of 95.55%. An average estimation error is 2.14 days.
      通信作者: 严洁, yan_jie@foxmail.com
    • 基金项目: 国家自然科学基金(批准号: 61602331)资助的课题
      Corresponding author: Yan Jie, yan_jie@foxmail.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61602331)
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    The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team 2020 Chin. J. Epidemiol. 41 145Google Scholar

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    Wang J, Wang L, Li X 2016 IEEE Trans. Cybernetics 46 2782Google Scholar

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    Ho H, Fraser C, Lam T, Ghani C, Leung G, Leung G, Chau Y K, Ho P L, Lo , Abu-Raddad L, Donnelly C, Anderson D, Chan K, Lee K, Lau E, Hedley A, RileyS, Tsang T, Ferguson N, Thach D T 2003 Science 300 1961Google Scholar

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  • 图 1  不同的$\beta $取值下实际累积发病人数与预测发病人数的对比 (a) 2019年; (b) 2020年

    Fig. 1.  Comparing the actual cumulative number of cases and its estimations according to different$\beta $: (a) Year 2019; (b) year 2020.

    图 2  武汉“封城”前夕迁徙指数与2019年的对比 (a)迁入规模指数; (b) 迁出规模指数

    Fig. 2.  Comparing the migration index of Wuhan before the spring festival with the same period of 2019: (a) Inner migration index; (b) outer migration index.

    图 3  各省区首达病例时间预测误差

    Fig. 3.  The estimation errors of the first arrival times for each provinces.

    表 1  2019年累积发病人数

    Table 1.  The cumulative number of confirmed cases in 2019.

    日期人数日期人数日期人数日期人数日期人数
    12/09112/171212/212912/254712/2978
    12/11212/181412/223712/264912/3090
    12/12512/191612/234012/275912/31102
    12/15812/202512/244512/2868
    下载: 导出CSV

    表 2  2020年各时间段累积发病人数

    Table 2.  The cumulative number of confirmed cases in each time slots in 2020.

    截至时点估计发病人数实际发病人数上报CCDC人数
    软件抓取法蒙特卡罗法
    2019/12/31102491020
    2020/01/10738459738—78141
    2020/01/20616258006143—6187291
    2020/01/31326612965432633—3267711821
    2020/02/1144692691634467244730
    下载: 导出CSV

    表 3  传染率$\beta $可能的取值

    Table 3.  Possible values of the infection rate.

    截止日期$\beta $置信区间R2截止日期$\beta $置信区间R2
    2019/12/310.2213[0.2152, 0.2274]0.8682020/01/110.2066[0.2056, 0.2274]0.990
    2020/01/010.2171[0.2116, 0.2225]0.8782020/01/120.2063[0.2056, 0.2071]0.993
    2020/01/020.2168[0.2127, 0.2209]0.92320200/1/130.2060[0.2054, 0.2067]0.995
    2020/01/030.2159[0.2127, 0.2191]0.9492020/01/140.2059[0.2054, 0.2064]0.997
    2020/01/040.2155[0.2130, 0.2179]0.9672020/01/150.2056[0.2052, 0.2060]0.998
    2020/01/050.2138[0.2118, 0.2159]0.9732020/10/160.2058[0.2054, 0.2061]0.998
    2020/01/060.2127[0.2109, 0.2144]0.9802020/01/170.2060[0.2057, 0.2063]0.999
    2020/01/070.2109[0.2093, 0.2126]0.9802020/01/180.2064[0.2061, 0.2066]0.999
    2020/01/080.2091[0.2075, 0.2107]0.9792020/01/190.2065[0.2063, 0.2067]0.999
    2020/01/090.2080[0.2067, 0.2094]0.9842020/01/200.2066[0.2064, 0.2068]0.999
    2020/01/100.2067[0.2054, 0.2080]0.9852020/01/210.2070[0.2068, 0.2073]0.999
    下载: 导出CSV

    表 4  重要时间节点的累积发病人数

    Table 4.  Cumulative confirmed cases in key time nodes.

    截至时点$\beta $
    0.22130.21590.20800.2066
    2019/12/311301169795
    2020/01/1011901001777753
    2020/01/2010870866662205964
    下载: 导出CSV

    表 5  武汉市三大火车站发送旅客人数与迁出指数

    Table 5.  The Baidu inner migration index and the number of the travelers sent from Wuhan`s major railway stations.

    日期迁徙指数人数/万日期迁徙指数人数/万日期迁徙指数人数/万
    2020/01/106.6232272020/01/2211.840329.962019/01/297.028227.2
    2020/01/117.561229.82019/01/214.571821.62019/01/307.107227.7
    2020/01/126.2165272019/01/224.689221.42019/01/317.480028.1
    2020/01/135.762024.82019/01/234.8062232019/02/018.714029.8
    2020/01/155.908726.52019/01/244.860521.72019/02/029.604331.5
    2020/01/166.002827.72019/01/267.0436272019/02/039.224729.1
    2020/01/197.4060302019/01/286.770626.8
    下载: 导出CSV

    表 6  省级区域的首例到达时间

    Table 6.  The arrival times of each provinces.

    省份$\beta $实际日期省份$\beta $实际日期
    0.22130.21590.20700.22130.21590.2070
    安徽01/0601/0601/0701/07辽宁01/1101/1201/1301/09
    北京01/0701/0701/0801/08*内蒙古01/1301/1401/1601/16
    福建01/0901/0901/1001/06宁夏01/1701/1801/2001/17
    甘肃01/1001/1101/1201/04青海01/1901/2101/2301/21
    广东01/0501/0501/0601/04山东01/0801/0801/0901/08
    广西01/0801/0901/0901/13山西01/0901/1001/1001/14
    贵州01/0801/0801/0901/06陕西01/0901/0901/1001/12
    海南01/1001/1101/1201/13上海01/0801/0801/0901/10
    河北01/0801/0901/0901/13四川01/0801/0801/0901/07
    河南01/0401/0401/0501/03天津01/1401/1501/1601/11
    黑龙江01/1201/1301/1401/12西藏 > 01/23 > 01/23 > 01/2301/30
    湖南01/0501/0501/0601/05新疆01/1201/1201/1401/17
    吉林01/1501/1501/1701/14云南01/0901/1101/1001/07
    江苏01/0601/0701/0701/10浙江01/0701/0701/0801/04
    江西01/0601/0701/0701/07重庆01/0801/0801/0901/06
    下载: 导出CSV
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    Zhang S, Diao M Y, Yu W B, Pei L, Lin Z F, Chen D C 2020 Int. J. Infect. Dis. 93 201Google Scholar

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    Yang Z F, Zeng Z Q, Wang K, Wong S S, Liang W H, Zanin M, Liu P, Cao X D, Gao Z Q, Mai Z T, Liang J Y, Liu X Q, Li S Y, Li Y M, Ye F, Guan W J, Yang Y F, Li F, Luo S M, Xie Y Q, Liu B, Wang Z L, Zhang S B, Wang Y N, Zhong N S, He J X 2020 J. Thorac. Dis. 12 2077

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    The Novel Coronavirus Pneumonia Emergency Response Epidemiology Team 2020 Chin. J. Epidemiol. 41 145Google Scholar

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    Ho H, Fraser C, Lam T, Ghani C, Leung G, Leung G, Chau Y K, Ho P L, Lo , Abu-Raddad L, Donnelly C, Anderson D, Chan K, Lee K, Lau E, Hedley A, RileyS, Tsang T, Ferguson N, Thach D T 2003 Science 300 1961Google Scholar

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出版历程
  • 收稿日期:  2020-02-25
  • 修回日期:  2020-03-11
  • 刊出日期:  2020-04-20

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