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传染病流行病学中基本再生数与有效再生数指标的研究进展

张晓宝 严丹莹 陈灿 蒋黛西 丁丞 蓝蕾 吴杰 杨仕贵

张晓宝, 严丹莹, 陈灿, 蒋黛西, 丁丞, 蓝蕾, 吴杰, 杨仕贵. 传染病流行病学中基本再生数与有效再生数指标的研究进展[J]. 中华疾病控制杂志, 2021, 25(7): 753-757, 790. doi: 10.16462/j.cnki.zhjbkz.2021.07.003
引用本文: 张晓宝, 严丹莹, 陈灿, 蒋黛西, 丁丞, 蓝蕾, 吴杰, 杨仕贵. 传染病流行病学中基本再生数与有效再生数指标的研究进展[J]. 中华疾病控制杂志, 2021, 25(7): 753-757, 790. doi: 10.16462/j.cnki.zhjbkz.2021.07.003
ZHANG Xiao-bao, YAN Dan-ying, CHEN Can, JIANG Dai-xi, DING Cheng, LAN Lei, WU Jie, YANG Shi-gui. Research progress on the basic and effective reproductive number in the epidemiology of infectious diseases[J]. CHINESE JOURNAL OF DISEASE CONTROL & PREVENTION, 2021, 25(7): 753-757, 790. doi: 10.16462/j.cnki.zhjbkz.2021.07.003
Citation: ZHANG Xiao-bao, YAN Dan-ying, CHEN Can, JIANG Dai-xi, DING Cheng, LAN Lei, WU Jie, YANG Shi-gui. Research progress on the basic and effective reproductive number in the epidemiology of infectious diseases[J]. CHINESE JOURNAL OF DISEASE CONTROL & PREVENTION, 2021, 25(7): 753-757, 790. doi: 10.16462/j.cnki.zhjbkz.2021.07.003

传染病流行病学中基本再生数与有效再生数指标的研究进展

doi: 10.16462/j.cnki.zhjbkz.2021.07.003
基金项目: 

国家自然科学基金 81672005

国家自然科学基金 U1611264

国家科技重大专项 2018ZX10715-014-002

科技部中青年科技创新领军人才 2017RA2120

详细信息
    通讯作者:

    杨仕贵,E-mail:yangshigui@zju.edu.cn

  • 中图分类号: R181

Research progress on the basic and effective reproductive number in the epidemiology of infectious diseases

Funds: 

National Natural Science Foundation of China 81672005

National Natural Science Foundation of China U1611264

National Science and Technology Major Project 2018ZX10715-014-002

Fund of Young and Middle-aged Scientific and technological innovation leaders of the Ministry of Science and Technology 2017RA2120

More Information
  • 摘要: 当一种新的传染病出现时,研究者们往往会用一些流行病学指标来衡量它的传播能力,其中一类重要的指标就是基本再生数(R0)和有效再生数(Re)。然而,R0Re的定义、计算方法和结果解释等在许多场景中被错误地理解,甚至误用。本文围绕R0Re的定义、计算方法、两者关系、影响因素、流行病学意义、应用注意事项以及常见传染病的基本再生数等进行综述,为卫生决策部门利用R0Re制定针对性疫情防控措施提供参考。
  • 表  1  常见传染病的基本再生数

    Table  1.   Basic reproductive numbers of common infectious diseases

    疾病 传播途径 时间(年) 地区 R0
    百日咳 空气、飞沫、接触 1908-1917 美国 12.20
    1944-1979 英格兰、威尔士 14.30~17.10 a
    麻疹 空气 1912 美国 12.5
    1944-1979 英格兰、威尔士 13.70~18.00 a
    1996 卢森堡 6.2~7.7 a
    天花 空气、飞沫 1967 尼日利亚 3.50~6.00 a
    SARS 空气、飞沫、粪口 2003 新加坡[20] 2.20~3.60 a
    2003 中国香港[21] 2.70 (2.20~3.70) b
    MERS c 空气、飞沫、接触 2013 英国、法国等[22] 0.60~0.69 a
    2013 沙特阿拉伯[23] 2.00~6.70 a
    EBHF d 体液 2014 几内亚[24] 1.51(1.50~1.52) b
    2014 塞拉利昂[24] 2.53 (2.41~2.67) b
    H1N1流感 空气、飞沫 1918 全球[25] 1.80 (1.47~2.27) b
    2009 全球[25] 1.46 (1.30~1.70) b
    2009 中国[26] 1.68 (1.45~1.92) b
    2009 印度[27] 1.03~1.75 a
    ZIKVD e 虫媒、体液、母婴 2007 雅普岛等[28] 2.10 (1.80~2.50) b
    2015 巴西[29-30] 1.80~5.80 a
    AIDS 性、血液、母婴 2009 法国 3.65 (3.64~3.66) b
    2009 西德 4.08 (4.02~4.14) b
    2009 英国 3.67 (3.66~3.69) b
    COVID-19 飞沫、接触、粪口 2020 中国[31] 1.40~3.58 a
    2020 韩国[32] 2.10 (1.84~2.42) b
    2020 钻石公主号游轮[33] 5.70 (4.23~7.79) b
      注:a R0值的范围,即Min~Max;b R0 (95% CI)值;c中东呼吸综合征(Middle East respiratory syndrome, MERS);d埃博拉出血热(ebola hemorrhagic ferer, EBHF);e寨卡病毒病(Zika virus diseases, ZIKVD)。
    下载: 导出CSV

    表  2  差分方程和Python软件实现代码

    Table  2.   Differential equation and implementation code in Python

    类别 描述
    差分方程 dS/dt=-βSI/N
    dE/dt=βSI/N-σE
    dI/dt=σE-γI
    dR/dt=γI
    实现代码 import scipy.integrate as spi
    import numpy as np
    import matplotlib.pyplot as plt
    N=11212000
    beta=0.6
    gamma=0.1
    Te=4.0
    I_0=1
    E_0=0
    R_0=0
    S_0=N-I_0-E_0-R_0
    T=160
    INI=(S_0, E_0, I_0, R_0)
    def funcSEIR(inivalue, _):
    Y=np.zeros(4)
    X=inivalue
    Y[0]=-(beta*X[0]*X[2])/N
    Y[1]=(beta*X[0]*X[2])/N-X[1]/Te
    Y[2]=X[1]/Te-gamma*X[2]
    Y[3]=gamma*X[2]
    return Y
    T_range=np.arange(0, T+1)
    RES=spi.odeint(funcSEIR, INI, T_range)
    plt.plot(RES[: , 0], color =’darkblue’, label=’Susceptible’, marker=’.’)
    plt.plot(RES[: , 1], color=’orange’, label=’Exposed’, marker=’.’)
    plt.plot(RES[: , 2], color =’red’, label=’Infection’, marker=’.’)
    plt.plot(RES[: , 3], color=’green’, label =’Recovery’, marker=’.’)
    plt.title(’SEIR Model’)
    plt.legend()
    plt.xlabel(’Day’)
    plt.ylabel(’Number’)
    plt.show()
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-08
  • 修回日期:  2021-06-24
  • 网络出版日期:  2021-08-13
  • 刊出日期:  2021-07-10

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