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SCIENTIA SINICA Mathematica, Volume 50 , Issue 7 : 969(2020) https://doi.org/10.1360/SSM-2020-0037

When will be the resumption of work in Wuhan and its surrounding areas during COVID-19 epidemic? A data-driven network modeling analysis

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  • ReceivedFeb 14, 2020
  • AcceptedFeb 17, 2020
  • PublishedFeb 20, 2020

Abstract

Based on the report of epidemic data sets for Hubei province and mainland China,the big data from Baidu population migration trends and distributions,we formulated the COVID-19 transmission model on complex networks for Wuhan city and the 15 surrounding cities with severe epidemics, and analyzed the possible times for resumption of work in Wuhan and its surrounding areas and the impact of resumption of work on the risk of a secondary outbreak. Firstly, we estimated the actual cumulative number of cases in Wuhan on January 23rd on the basis of the cumulative number of reported cases in other 15 cities, and obtained the control reproduction numbers for the 16 major cities in Hubei province in different periods. Our research results revealed that the early transmission risk in these areas is high and the current transmission risk is low (due to the control reproduction numbers being less than 1). By simulating the whole network model on the flow network structure and flow volume in the same period of last year, we investigated the impact of the resumption of work on February 17, February 24 and March 2 on disease infection for each city. Main conclusion showed that with strong prevention measures and self-protection the second outbreak will not be caused during a period by the resumption of work on March 2, 2020.


Funded by

国家自然科学基金(11631012,61772017和11601301)


Acknowledgment

特别感谢审稿人提出的宝贵意见,感谢研究生杨洁和赵吴琼在研究期间收集数据所付出的努力.


References

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  • Table 1   各城市总人口数
    武汉 孝感 黄冈 荆州 咸宁 鄂州 襄阳 黄石
    11081000 5300000 7500000 6410000 2535100 1076900 6050000 2689300
    $S_1(0)$ $S_2(0)$ $S_3(0)$ $S_4(0)$ $S_5(0)$ $S_6(0)$ $S_7(0)$ $S_8(0)$
    荆门 随州 仙桃 宜昌 天门 恩施州 十堰 潜江
    3000000 2216700 1563500 4169200 1609200 4026100 3406000 962000
    $S_9(0)$ $S_{10}(0)$ $S_{11}(0)$ $S_{12}(0)$ $S_{13}(0)$ $S_{14}(0)$ $S_{15}(0)$ $S_{16}(0)$
  • Table 2   参数定义和估计值
    参数 定义 参数值 来源
    $c$ 接触率 13.0046 参数估计
    $\beta$ 每次接触传播的概率 $2.0389\times~10^{-9}$ 参数估计
    $q~$ 隔离率 $1.8877\times~10^{-7}$ 参数估计
    $\sigma$ 潜伏者到感染者的转移率 1/5 文献[9]
    $\lambda$ 隔离的未受感染接触者释放回社区的速率 1/14 文献 [7,10]
    $\rho$ 感染者有症状的概率 0.6834 参数估计
    $\delta_{I}$ 有症状的感染者被隔离的速率 0.1328 参数估计
    $\delta_{q}$ 隔离的潜伏者变为隔离的感染者的速率 0.1259 参数估计
    $\gamma_{I}$ 有症状的感染者的恢复率 0.1029 参数估计
    $\gamma_{A}$ 无症状感染者的恢复率 0.2978 参数估计
    $\gamma_{H}$ 隔离的感染者的恢复率 0.1024 参数估计
    $\alpha$ 因病死亡率 0.0009 参数估计
    $\theta$ 无症状感染者接触率调节因子 1.6003 参数估计
    $\nu$ 潜伏者接触率调节因子 1.5008 参数估计
    初值 定义 参数值 来源
    $S_1(0)$ 易感者的初值 11081000 文献[9]
    $E_1(0)~$ 潜伏者的初值 600.0110 参数估计
    $I_1(0)$ 有症状感染者的初值 409.9978 参数估计
    $A_1(0)$ 无症状感染者的初值 30.0278 参数估计
    $S_{q1}(0)$ 隔离的易感者的初值 739 数据
    $E_{q1}(0)$ 隔离的潜伏者的初值 20 参数估计
    $H_1(0)$ 隔离的感染者的初值 41 数据
    $R_1(0)$ 恢复者的初值 2 数据
  • Table 3   各城市参数 $\boldsymbol{c}$ 和 $\boldsymbol{q}$ 的估计值及再生数 (其中下标1、2和3分别表示三个时间段)
    城市 武汉 孝感 黄冈 荆州 咸宁 鄂州 襄阳 黄石
    $c_1$ 13.40 15.56 12.36 12.14 32.65 70.00 18.63 34.01
    $q_1$ $1.89\times~10^{-7}$ $1.09\times~10^{-9}$ $1.05\times~10^{-9}$ $1.27\times~10^{-9}$ $7.86\times~10^{-7}$ $1.09\times~10^{-9}$ $9.73\times~10^{-8}$ $1.33\times~10^{-9}$
    $c_2$ 4.48 13.50 2.00 33.35 5.01 66.55 0.10 30.02
    $q_2$ $4.13\times~10^{-6}$ $1.09\times~10^{-6}$ $2.46\times~10^{-6}$ $1.00\times~10^{-5}$ $4.70\times~10^{-6}$ $2.12\times~10^{-9}$ $1.00\times~10^{-5}$ $6.07\times~10^{-6}$
    $c_3$ 4.48 $1.03\times~10^{-4}$ 4.46 1.60 0.01 32.99 0.01 $29.98$
    $q_3$ $4.13\times~10^{-6}$ $1.00\times~10^{-3}$ $1.00\times~10^{-3}$ $1.00\times~10^{-3}$ $1.03\times~10^{-3}$ $1.00\times~10^{-4}$ $1.01\times~10^{-5}$ $1.08\times~10^{-5}$
    $R_{c1}$ 3.66 2.03 2.28 1.92 2.04 1.86 2.78 2.26
    $R_{c2}$ 0.41 1.91 0.39 5.44 0.28 1.98 0.01 2.08
    $R_{c3}$ 0.09 $9.49\times~10^{-6}$ 0.77 0.02 $5.00\times~10^{-4}$ 0.98 $1.50\times~10^{-3}$ $0.50$
    城市 荆门 随州 仙桃 宜昌 天门 恩施州 十堰 潜江
    $c_1$ 42.77 50.98 37.93 26.91 47.99 21.89 35.94 60.01
    $q_1$ $2.75\times~10^{-6}$ $1.04\times~10^{-9}$ $2.11\times~10^{-9}$ $7.07\times~10^{-8}$ $1.58\times~10^{-6}$ $2.77\times~10^{-6}$ $1.76\times~10^{-6}$ $9.49\times~10^{-7}$
    $c_2$ 1.01 8.00 70.99 1.00 47.99 1.00 1.00 50.02
    $q_2$ $1.00\times~10^{-5}$ $1.27\times~10^{-6}$ $1.88\times~10^{-9}$ $1.00\times~10^{-5}$ $6.78\times~10^{-6}$ $1.02\times~10^{-46}$ $1.00\times~10^{-5}$ $1.52\times~10^{-9}$
    $c_3$ 1.01 0.10 24.38 0.03 47.98 0.01 0.01 2.00
    $q_3$ $9.46\times~10^{-4}$ $9.99\times~10^{-4}$ $1.00\times~10^{-3}$ $9.86\times~10^{-4}$ $1.00\times~10^{-3}$ $1.05\times~10^{-3}$ $9.68\times~10^{-4}$ $1.52\times~10^{-9}$
    $R_{c1}$ 3.61 2.79 1.46 2.77 1.90 2.17 3.01 1.42
    $R_{c2}$ 0.03 0.46 2.90 0.10 1.67 0.09 0.06 1.17
    $R_{c3}$ 0.04 $5.00\times~10^{-3}$ 0.99 $2.80\times~10^{-3}$ 0.83 $7.54\times~10^{-4}$ $6.33\times~10^{-4}$ 0.05

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