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评估新型冠状病毒地区防控效果的一种近似方法

李冀鹏 洪峰 白薇 廖敬仪 张彦如 周涛

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评估新型冠状病毒地区防控效果的一种近似方法

李冀鹏, 洪峰, 白薇, 廖敬仪, 张彦如, 周涛

Approximate method to evaluate the regional control efficacy of COVID-19

Li Ji-Peng, Hong Feng, Bai Wei, Liao Jing-Yi, Zhang Yan-Ru, Zhou Tao
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  • 我们观察到地区累计确诊的病例数目和武汉封城前流入的人口总数高度相关, 且本地第三代感染者占比很小. 基于此, 提出了一种考虑输入病例和地区人口效应的定量化评估新型冠状病毒地区防控效果的近似方法, 并将其用于评估武汉流出人口前50的城市防控的成效. 防控效果最显著的10 个城市依次是石家庄、洛阳、恩施、周口、厦门、贵阳、咸宁、安庆、信阳、南宁.
    The cumulative number of local confirmed cases was highly correlated with the total inflow population from Wuhan before the city closure, and the proportion of third-generation infections in a local region is tiny. Accordingly, we proposed an approximate method to quantitatively evaluate the regional control efficacy of COVID that takes into account effects of both imported cases and regional population. We applied this method to evaluate the control efficacy of the top-50 cities with maximum inflow population from Wuhan. The 10 cities with the most significant control efficacy are Shijiazhuang, Luoyang, Enshi, Zhoukou, Xiamen, Guiyang, Xianning, Anqing, Xinyang, and Nanning.
      通信作者: 周涛, zhutou@ustc.edu
      Corresponding author: Zhou Tao, zhutou@ustc.edu
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    中国疾病预防控制中心新型冠状病毒肺炎应急响应机制流行病学组 2020 中华流行病学杂志 41 145Google Scholar

    Epidemiology group of covid-19 emergency response mechanism, Chinese center for disease control and prevention 2020 Chinese Journal of Epidemiology 41 145Google Scholar

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    栾荣生, 王新, 孙鑫, 陈兴蜀, 周涛, 刘权辉, 吕欣, 吴先萍, 谷冬晴, 唐明霜 2020 四川大学学报(医学版) 51 131

    Luan R S, Wang X, Sun X, Chen X S, Zhou T, Liu Q H, Lu X, Wu X P, Gu D Q, Tang M S 2020 J. Sichuan University (Medical Edition) 51 131

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    Du Z W, Wang L, Cauchemez S, Xu X K, Wang X W, Cowling B J, Meyers L A 2020 Emerging Infectious Diseases 2020 26

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    Hethcote H W 2020 SIAM Rev. 42 599

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    Pastor-Satorras R, Castellano C, Van M P, Vespignani A 2015 Phys. Rev. 87 925

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    Dunbar R I M 1992 J. Human Evol. 22 469Google Scholar

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    Wang Q, Gao J, Zhou T, Hu Z, Tian H 2016 EPL 114 58004Google Scholar

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    Zhou T, Liu J G, Bai W J, Chen G, Wang B H 2006 Phys. Rev. E 74 056109Google Scholar

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  • 图 1  武汉流入人口最多的50 个城市的累计确诊数(人)与武汉流入人口数(万人)之间的关系. 其中数据点代表城市, 红色直线代表线性拟合的结果(R2 = 0.942)

    Fig. 1.  The relationship between the cumulative number of confirmed cases in the top-50 cities with maximum inflow population from Wuhan and the number of corresponding inflow people. Cities are represented by data points and the linear fitting is represented by the red line (R2 = 0.942).

    图 2  双对数坐标下(Ni uAi)/uAiPi的关联关系. 其中数据点代表城市, 红色直线代表线性拟合的结果(R2 = 0.141), 拟合的斜率是0.234

    Fig. 2.  The correlation between (NiuAi)/uAi and Pi in the log-log coordinates, where data points represent cities and the red line represents the linear fitting (R2 = 0.141). The fitting slope is 0.234.

    图 3  不同a值所得到的50 个城市防控效果排序的Kendall’s Tau值

    Fig. 3.  Kendall's Tau between rankings of control efficacy for different a.

    表 1  武汉封城前2 周流入人口前50的城市名称、流入人口数、常住人口数、截止到2020年2 月25 日的累计确诊人数、控制因子c的取值以及利用本文方法所得到的防控效果的排名. 武汉流入人口统计的是2020 年1 月10 日至1 月22 日离开武汉的人数, 数据来源于“百度迁徙”. 常住人口数取自第六次全国人口普查数据(http://www.stats.gov.cn/tjsj/pcsj/rkpc/6rp/indexch.htm)

    Table 1.  The six columns respectively show the names of the top-50 cities with maximum inflow population from Wuhan during the two weeks before the closure, the inflow population, the permanent resident population, the cumulative number of confirmed cases as of February 25, 2020, the values of the controlling parameter c, and the rankings of the control efficacy by the present method. The inflow population accounts for the number of people who left Wuhan from January 10 to January 22, 2020, obtained from “Baidu Migration”. The number of permanent residents is taken from the sixth national census (http://www.stats.gov.cn/tjsj/pcsj/rkpc/6rp/indexch.htm).

    城市名称武汉流入人数 (万人)常住人口数 (万人)累计确诊人数控制因子c的取值防控效果排名
    孝感市65.620492.00034820.075826
    黄冈市63.630633.00029040.057918
    荆州市31.660559.02015760.067422
    咸宁市25.340254.3308360.04307
    鄂州市20.525107.77013850.148145
    襄阳市19.240566.90011750.088431
    黄石市18.875247.07010080.089833
    荆门市15.460289.6509200.100037
    随州市14.980221.67013050.171047
    仙桃市14.345114.0005750.071324
    宜昌市13.850413.5859260.106838
    天门市10.165127.2304950.092435
    恩施市9.310337.8002510.02753
    十堰市8.975340.6006710.128541
    信阳市7.190647.4102740.04399
    重庆市6.6203101.7905760.092134
    长沙市5.755815.4702420.048413
    潜江市5.61096.2001950.059020
    北京市5.1302154.2004000.087930
    上海市3.8552423.7803360.097836
    郑州市3.3851013.6001570.053116
    南阳市3.3601001.3601550.052815
    驻马店市3.320805.1801390.048212
    九江市2.720489.6801180.057117
    广州市2.6601490.4403460.173848
    成都市2.6501604.4701430.058819
    深圳市2.6101302.6604170.225349
    岳阳市2.560579.7101560.087729
    南昌市2.490554.5502290.147144
    安庆市2.310469.100830.04308
    合肥市2.260808.7001740.108839
    周口市2.190867.780760.03524
    西安市1.8551000.3701200.083327
    南京市1.845843.620930.062321
    阜阳市1.6901036.0001690.140243
    杭州市1.690820.7001550.133842
    商丘市1.655732.530910.072525
    常德市1.580582.700820.070723
    宜春市1.455555.3701060.111040
    南宁市1.405725.410550.044610
    苏州市1.3151072.170870.084428
    昆明市1.245685.000530.051314
    衡阳市1.215720.530480.045311
    温州市1.160925.0005040.704050
    六安市1.155483.700690.089132
    天津市1.1401559.6001350.154746
    石家庄市1.1351103.120290.01861
    洛阳市1.120688.850310.02452
    贵阳市1.120488.190360.03536
    厦门市1.115411.000350.03525
    下载: 导出CSV
  • [1]

    Wu J T, Leung K, Leung G M 2020 LANCET 395 689Google Scholar

    [2]

    Vincent J M, Marion K, Neeltje V D, Debby V R, Emmie D W 2020 N. Engl. J. Med. 382 692Google Scholar

    [3]

    Zhu N, Zhang D Y, Wang W L, Li X W, Yang B 2019 N. Engl. J. Med. 382 727

    [4]

    中国疾病预防控制中心新型冠状病毒肺炎应急响应机制流行病学组 2020 中华流行病学杂志 41 145Google Scholar

    Epidemiology group of covid-19 emergency response mechanism, Chinese center for disease control and prevention 2020 Chinese Journal of Epidemiology 41 145Google Scholar

    [5]

    栾荣生, 王新, 孙鑫, 陈兴蜀, 周涛, 刘权辉, 吕欣, 吴先萍, 谷冬晴, 唐明霜 2020 四川大学学报(医学版) 51 131

    Luan R S, Wang X, Sun X, Chen X S, Zhou T, Liu Q H, Lu X, Wu X P, Gu D Q, Tang M S 2020 J. Sichuan University (Medical Edition) 51 131

    [6]

    Adnerson R M, May R M 1991 OUP. OX.

    [7]

    Li Q, Guan X H, Wu P, Wang X Y, Zhou L, Tong Y Q, Ren R Q, Kathy S M L, Eric H Y L, Jessica Y W, Xing X S, Xiang N J, Wu Y, Li C, Chen Q, Li D, Liu T, Zhao J, Liu M, Tu W X, Chen C D, Jin L M, Yang R, Wang Q, Zhou S H, Wang R, Liu H, Luo Y B, Liu Y, Shao G E, Li H, Tao Z F, Yang Y, Deng Z Q, Liu B X, Ma Z T, Zhang Y P, Shi G Q, Tommy T Y L, Joseph T W, George F G, Benjamin J C, Yang B, Gabriel M L, Feng Z J 2020 N. Engl. J. Med. 382 727Google Scholar

    [8]

    Jonathan M R, Jessica R E B, Derek A T C, Antonia H, Chris P J 2020 MedRxiv 20018549

    [9]

    Majumder M, Mandl K D 2020 SSRN 3524675

    [10]

    Natsuko I, Anne C, Ilaria D, Marc B, Christl A D, Steven R, Neil M F 2020 Imperial College London

    [11]

    Liu T, Hu J, Kang M, Lin L, Zhong H, Xiao J, He G, Song T, Huang Q, Rong Z 2020 bioRxiv 919787

    [12]

    Riou J, Althaus C L 2020 Eurosurveillance 25 2000058

    [13]

    Zhou T, Liu Q H, Yang Z M, Liao J Y, Yang K X, Bai W, Lu X, Zhang W 2020 Journal of Evidence-Based Medicine 13 3Google Scholar

    [14]

    宋倩倩, 赵涵, 方立群, 刘玮, 郑创, 张勇 2020 中华流行病学杂志 41 461Google Scholar

    Song Q Q, Zhao H, Fang L Q, Liu W, Zheng C, Zhang Y 2020 Chinese Journal of Epidemiology 41 461Google Scholar

    [15]

    Zhang J, Litvinova M, Wang W, Wang Y, Deng X, Chen X,Li M, Zheng W, Yi L, Chen X 2020 medRxiv 2002632 8

    [16]

    Chen D B, Zhou T arXiv 2003.00305

    [17]

    陈端兵, 白薇, 王岩, 王敏, 俞伍平, 周涛 2020 电子科技大学学报

    Chen D B, Bai W, Wang Y, Wang M, Yu W P, Zhou T 2020 Journal of University of Electronic Science and Technology of China (in Press) (in Chinese)

    [18]

    许小可, 文成, 张光耀, 孙皓宸, 刘波, 王贤文 2020 电子科技大学学报

    Xu X K, Wen C, Zhang G Y, Sun H C, Liu B, Wang X W 2020 Journal of University of Electronic Science and Technology of China (in Press) (in Chinese)

    [19]

    杨政, 原子霞, 贾祖瑶 2020 电子科技大学学报

    Yang Z, Yuan Z X, Jia Z Y 2020 Journal of University of Electronic Science and Technology of China (in Press) (in Chinese)

    [20]

    Du Z W, Wang L, Cauchemez S, Xu X K, Wang X W, Cowling B J, Meyers L A 2020 Emerging Infectious Diseases 2020 26

    [21]

    Hethcote H W 2020 SIAM Rev. 42 599

    [22]

    Pastor-Satorras R, Castellano C, Van M P, Vespignani A 2015 Phys. Rev. 87 925

    [23]

    Dunbar R I M 1992 J. Human Evol. 22 469Google Scholar

    [24]

    Wang Q, Gao J, Zhou T, Hu Z, Tian H 2016 EPL 114 58004Google Scholar

    [25]

    Zhou T, Liu J G, Bai W J, Chen G, Wang B H 2006 Phys. Rev. E 74 056109Google Scholar

    [26]

    Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189Google Scholar

    [27]

    Yang R, Zhou T, Xie Y B, Lai Y C, Wang B H 2008 Phys. Rev. E 78 066109Google Scholar

    [28]

    Balcan D, Gonçalves B, Hu H, Ramasco J J, Vittoria C, Alessandro V 2010 J. Comput.Sci. 1 132Google Scholar

    [29]

    Liu Q H, Ajelli M, Aleta A, Merler S, Moreno Y, Vespignani A 2018 PNAS 115 12680Google Scholar

    [30]

    Li R, Pei S, Chen B, Song Y, Zhang T, Yang W, Shaman J 2020 Science 368 489Google Scholar

    [31]

    闫小勇 2020 物理学报 69 088904

    Yan X Y 2020 Acta Phys. Sin. 69 088904

    [32]

    Kendall M 1938 Biometrika 30 81Google Scholar

    [33]

    Goltsev A V, Dorogovtsev S N, Oliveira J G, Mendes J F F 2012 Phys. Rev. Lett. 109 128702Google Scholar

    [34]

    Um J, Son S W, Lee S I, Jeong H, Kim B J 2012 PNAS 106 14236

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    [20] 欧阳成. 电流变液系统流动的渐近估计. 物理学报, 2004, 53(6): 1900-1902. doi: 10.7498/aps.53.1900
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出版历程
  • 收稿日期:  2020-03-14
  • 修回日期:  2020-05-15
  • 刊出日期:  2020-05-20

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