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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.
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Keywords:
- COVID-19 /
- control efficacy /
- population flow
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Google Scholar
[2] Vincent J M, Marion K, Neeltje V D, Debby V R, Emmie D W 2020 N. Engl. J. Med. 382 692
Google 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 41 145
Google Scholar
Epidemiology group of covid-19 emergency response mechanism, Chinese center for disease control and prevention 2020 Chinese Journal of Epidemiology 41 145
Google 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. 382 727
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[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 3
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[14] 宋倩倩, 赵涵, 方立群, 刘玮, 郑创, 张勇 2020 中华流行病学杂志 41 461
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Song Q Q, Zhao H, Fang L Q, Liu W, Zheng C, Zhang Y 2020 Chinese Journal of Epidemiology 41 461
Google 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
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[25] Zhou T, Liu J G, Bai W J, Chen G, Wang B H 2006 Phys. Rev. E 74 056109
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[27] Yang R, Zhou T, Xie Y B, Lai Y C, Wang B H 2008 Phys. Rev. E 78 066109
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Yan X Y 2020 Acta Phys. Sin. 69 088904
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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) Figure 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)/uAi与Pi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
Figure 2. The correlation between (Ni – uAi)/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
Figure 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 65.620 492.000 3482 0.0758 26 黄冈市 63.630 633.000 2904 0.0579 18 荆州市 31.660 559.020 1576 0.0674 22 咸宁市 25.340 254.330 836 0.0430 7 鄂州市 20.525 107.770 1385 0.1481 45 襄阳市 19.240 566.900 1175 0.0884 31 黄石市 18.875 247.070 1008 0.0898 33 荆门市 15.460 289.650 920 0.1000 37 随州市 14.980 221.670 1305 0.1710 47 仙桃市 14.345 114.000 575 0.0713 24 宜昌市 13.850 413.585 926 0.1068 38 天门市 10.165 127.230 495 0.0924 35 恩施市 9.310 337.800 251 0.0275 3 十堰市 8.975 340.600 671 0.1285 41 信阳市 7.190 647.410 274 0.0439 9 重庆市 6.620 3101.790 576 0.0921 34 长沙市 5.755 815.470 242 0.0484 13 潜江市 5.610 96.200 195 0.0590 20 北京市 5.130 2154.200 400 0.0879 30 上海市 3.855 2423.780 336 0.0978 36 郑州市 3.385 1013.600 157 0.0531 16 南阳市 3.360 1001.360 155 0.0528 15 驻马店市 3.320 805.180 139 0.0482 12 九江市 2.720 489.680 118 0.0571 17 广州市 2.660 1490.440 346 0.1738 48 成都市 2.650 1604.470 143 0.0588 19 深圳市 2.610 1302.660 417 0.2253 49 岳阳市 2.560 579.710 156 0.0877 29 南昌市 2.490 554.550 229 0.1471 44 安庆市 2.310 469.100 83 0.0430 8 合肥市 2.260 808.700 174 0.1088 39 周口市 2.190 867.780 76 0.0352 4 西安市 1.855 1000.370 120 0.0833 27 南京市 1.845 843.620 93 0.0623 21 阜阳市 1.690 1036.000 169 0.1402 43 杭州市 1.690 820.700 155 0.1338 42 商丘市 1.655 732.530 91 0.0725 25 常德市 1.580 582.700 82 0.0707 23 宜春市 1.455 555.370 106 0.1110 40 南宁市 1.405 725.410 55 0.0446 10 苏州市 1.315 1072.170 87 0.0844 28 昆明市 1.245 685.000 53 0.0513 14 衡阳市 1.215 720.530 48 0.0453 11 温州市 1.160 925.000 504 0.7040 50 六安市 1.155 483.700 69 0.0891 32 天津市 1.140 1559.600 135 0.1547 46 石家庄市 1.135 1103.120 29 0.0186 1 洛阳市 1.120 688.850 31 0.0245 2 贵阳市 1.120 488.190 36 0.0353 6 厦门市 1.115 411.000 35 0.0352 5 
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[1] Wu J T, Leung K, Leung G M 2020 LANCET 395 689
Google Scholar
[2] Vincent J M, Marion K, Neeltje V D, Debby V R, Emmie D W 2020 N. Engl. J. Med. 382 692
Google 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 41 145
Google Scholar
Epidemiology group of covid-19 emergency response mechanism, Chinese center for disease control and prevention 2020 Chinese Journal of Epidemiology 41 145
Google 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. 382 727
Google 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 3
Google 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 41 461
Google Scholar
Song Q Q, Zhao H, Fang L Q, Liu W, Zheng C, Zhang Y 2020 Chinese Journal of Epidemiology 41 461
Google 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. 22 469
Google Scholar
[24] Wang Q, Gao J, Zhou T, Hu Z, Tian H 2016 EPL 114 58004
Google Scholar
[25] Zhou T, Liu J G, Bai W J, Chen G, Wang B H 2006 Phys. Rev. E 74 056109
Google Scholar
[26] Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T 2007 Phys. Lett. A 364 189
Google Scholar
[27] Yang R, Zhou T, Xie Y B, Lai Y C, Wang B H 2008 Phys. Rev. E 78 066109
Google Scholar
[28] Balcan D, Gonçalves B, Hu H, Ramasco J J, Vittoria C, Alessandro V 2010 J. Comput.Sci. 1 132
Google Scholar
[29] Liu Q H, Ajelli M, Aleta A, Merler S, Moreno Y, Vespignani A 2018 PNAS 115 12680
Google Scholar
[30] Li R, Pei S, Chen B, Song Y, Zhang T, Yang W, Shaman J 2020 Science 368 489
Google 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 81
Google Scholar
[33] Goltsev A V, Dorogovtsev S N, Oliveira J G, Mendes J F F 2012 Phys. Rev. Lett. 109 128702
Google Scholar
[34] Um J, Son S W, Lee S I, Jeong H, Kim B J 2012 PNAS 106 14236
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