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一种新型冠状病毒感染导致的肺炎自2019年12月至今在我国以及200多个国家和地区传播. 本文旨在介绍近期关于新型冠状病毒肺炎的几个重要流行病学参数的研究进展和估计方法, 包括基本再生数、潜伏期和代间隔, 同时还介绍两个动力学模型及其结果. 这些参数刻画了新型冠状病毒肺炎的传播特点, 影响控制策略的制定和有效性. 简要来说, 新型冠状病毒肺炎的基本再生数
${\cal{R}}_0$ 的中位数为2.6, 潜伏期均值约为5.0 d, 代间隔均值约为5.5 d. 这表明新型冠状病毒肺炎传播速度快. 诸如对确诊病人的隔离治疗、对疑似病例的隔离、对密切接触者的追踪、对疾病信息的宣传和采取自我防护等防控措施能有效降低疾病暴发的风险和规模.The coronavirus disease 2019 (COVID-19) has become a major public health concern internationally. To capture the epidemic growing patterns and quantify the transmissibility, some key epidemiological parameters and dynamic models are of significance for helping us to understand the features of COVID-19 and thus informing the strategic decision-making in combating the outbreak. In this study, we review and summarize the recently released research results about the reproduction numbers, incubation period and serial interval of COVID-19. We summarize the estimates as well as estimation approaches adopted to calculate these epidemiological parameters in the existing literature. These studies found that the basic reproduction number is estimated at 2.6, the mean incubation period at about 5.0 days, and the mean serial interval at about 5.5 days. The COVID-19 infections can increase rapidly if it is not controlled. The control measures including the isolation, quarantine, contact tracing, improvement of public awareness, and adoption of self-protection measures can effectively mitigate the COVID-19 outbreak.-
Keywords:
- coronavirus disease 2019 /
- basic reproduction number /
- incubation period /
- serial interval /
- dynamic model
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图 1 (a)每日新增病例模拟与确诊报告对比; (b) 每日确诊报告率
Fig. 1. (a) Daily new cases simulated versus reporting; (b) daily reporting rate
图 2 累积病例最多的前20个国家的日确诊病例和瞬时再生数的曲线关系图
Fig. 2. Curves of daily confirmed cases and instantaneous reproductive number of the top 20 countries with the most cumulative cases
图 3 累积病例最多的第21—40国家的日确诊病例和瞬时再生数的曲线图
Fig. 3. Curves of daily confirmed cases and instantaneous reproductive number of the 21st − 40th countries with the most cumulative cases.
表 1 不同模型或分布下的基本再生数
${\cal{R}}_{0}$ 的计算公式Table 1. The formula of the basic reproduction number
${\cal{R}}_{0}$ under different models or distributions.模型或分布 公式 参数介绍 $\rm {SIR}$模型 $ {\cal{R} }_{0}=1+ {r}/{b} $ r为增长率, b为移出率 ${\rm {SEIR}}$模型 ${\cal{R} }_{0}=\left(1+ {r}/{b_1}\right)\left(1+ {r}/{b_2}\right)$ $b_1, $ $ b_2$分别为从E, I 的移出率 多阶段暴露
与感染模型${\cal{R} }_{0}=\dfrac{\left(1+\dfrac{r}{b_1}\right)^x}{\displaystyle\sum\limits_{i=1}^{y}\left(1+\dfrac{r}{b_2}\right)^{-i} }$ $b_1, $ $b_2$为暴露x,
感染 y 阶段移出率正态分布 ${\cal{R} }_{0}=\exp\left(rT_{\rm c}-\dfrac{1}{2}r^2\sigma^2\right)$ $T_{\rm c}$为代间隔均值, $\sigma$为方差 德尔塔分布 ${\cal{R} }_{0}={\rm e}^{rT_{\rm c}}$ $T_{\rm c}$为代间隔均值 经验分布 ${\cal{R} }_{0}=\dfrac{r}{\displaystyle\sum\limits_{i=1}^{n}y_i\dfrac{ {\rm e }^{-ra_{i-1} }-{\rm e}^{-ra_i} }{a_i-a_{i-1} } }$ ai与$y_i$分别表示年龄与相应频率 
下载: 导出CSV
表 2 新冠肺炎基本再生数
${\cal{R}}_{0}$ 总结Table 2. Summary of the basic reproduction number
${\cal{R}}_{0}$ for COVID-19.地点 ${\cal{R}}_0$ 置信区间 截止时间 计算方法 参考文献 武汉市 2.2 [1.40, 2.20] 2020/01 临床诊断推断 [2] 武汉市 2.68 [2.47, 2.86] 2020/01/28 MCMC [3] 武汉市 4.08 — 2020/01/26 有效再生数${\cal{R}}_{\rm{e}}$ [5] 武汉市 3.0 [0.75, 7.80] 2020/01/24 统计推断 [16] 武汉市 6.47 [5.71, 7.23] 2020/01/15 统计推断 [17] 武汉市 2.56 [2.49, 2.63] 2020/01/24 极大似然 [18] 武汉市 2.3 — 2020/01/24 有效再生数${\cal{R}}_{\rm{e}}$ [19] 武汉市 2.23 [1.77, 3.00] 2020/01/24 有效再生数${\cal{R}}_{\rm{e}}$ [20] 武汉市 7.05 [6.11, 8.18] 2020/02/08 最大似然 [21] 湖北省 2.56 [4.70, 6.60] 2020/01/25 SEIR仓室模型 [22] 武汉市 2.24 [1.96, 2.25] 2020/01/24 极大似然 [23] 注: 表2—表4中参考文献数据均来自国家卫健委、湖北卫健委、中国CDC等网站及已发表文献.
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[1] Huang C L, Wang Y M, Li X W, et al. 2020 Lancet 20 301835
[2] Li Q, Guan X H, Wu P, et al. 2020 N. Engl. J. Med. 2020 2001316
Google Scholar
[3] Joseph T W, Kathy L, Gabriel M L 2020 Lancet 20 302609
[4] van den Driessche P, Watmough J 2002 Math. Biosci. 180 29
Google Scholar
[5] Cao Z D, Zhang Q P, Lu X 2020 medRxiv: 01.27.20018952
[6] Backer J A, Klinkenberg D, Wallinga J 2020 Euro. Surveill. 25 2000062
[7] Linton N M, Kobayashi T, Yang Y 2020 J. Clin. Med. 9 538
Google Scholar
[8] Leung C 2020 medRxiv: 02.13.20022822 v1
[9] Wallinga J, Lipsitch M 2007 Proc. R. Soc. B 274 599
Google Scholar
[10] Svensson Å 2007 Math. Biosci. 208 300
Google Scholar
[11] Guan W J, Ni Z Y, Hu Y, et al. 2020 N. Engl. J. Med. 2020 2002032
Google Scholar
[12] Ma S J, Zhang J Y, Zeng M Y, et al. 2020 bioRxiv: 03.21.20040329 v1
[13] Zhao S, Zhuang Z A, Cao P H, et al. 2020 J. Travel Med. 27 2002
Google Scholar
[14] Lai, S J, Bogoch I, Nick R, Alexander W, Lu X, Yang W Z, Yu H J, Kamran K, Andrew J T 2020 medRxiv: 02.04.20020479 v2
[15] Zhao S, Zhuang Z A, Ran J J, Gao D Z, Yang L, Cai Y L, Wang W M, He D H, Maggie H W 2020 Travel Med. Infect. Dis. 33 101568
Google Scholar
[16] Hiroshi N, Natalie M L, Andrei R A 2020 J. Clin. Med. 9 488
Google Scholar
[17] Tang B, Wang X, Li Q, Nicola L B, Tang S Y, Xiao Y N, Wu J H 2020 J. Clin. Med. 9 462
Google Scholar
[18] Zhao S, Salihu S M, Lin Q Y, Ran J J, Yang G P, Wang W W, Lou Y J, Gao D Z, He D H, Maggie H W 2020 J. Clin. Med. 9 388
Google Scholar
[19] Tuite A R, Fisman D N 2020 Ann. Internal Med. 2020 200358
Google Scholar
[20] Li R Y, Pei S, Chen B, Song Y M, Zhang T, Yang W, Jeffrey S 2020 Science DOI: 10.1126/science.abb3221Google Scholar
[21] Mizumoto K, Kagaya K, Chowell G 2020 medRxiv: 02.12.20022434 v1
[22] Sanche S, Lin Y T, Xu C G, Ehtan R S, Nick H, Rui A K 2020 medRxiv: 02.07.20021154 v1
[23] Zhao S, Lin Q Y, Ran J J, Salihu S M, Yang G P, Wang W M, Lou Y J, Gao D Z, Yang L, He D H 2020 Int. J. Infect. Dis. 92 214
Google Scholar
[24] You C, Deng Y H, Hu W J, Sun J R, Lin Q S, Zhou F, Pang C H, Zhang Y, Chen Z C, Zhou X N 2020 medRxiv: 02.08.20021253 v2
[25] Nishiura H, Linton N M, Akhmetzhanov 2020 medRxiv: 02.03.20019497 v2
[26] He D H, Dushoff J, Day T, Ma J L, Earn D J D 2013 Proc. R. Soc. B 280 20131345
Google Scholar
[27] Lin Q Y, Zhao S, Gao D Z, Lou Y J, Yang S, Salihu S M, Maggie H W, Wang W M, He D H 2020 Int. J. Infect. Dis. 93 211
Google Scholar
[28] Zhao S, Stone L, Gao D Z, Salihu S M, Marc K C, He D H 2020 Ann. Transl. Med. 2020 21037
Google Scholar
[29] Ma J L, Earn D J D 2006 Bull. Math. Biol. 68 679
Google Scholar
[30] 王霞, 唐三一, 陈勇, 冯晓梅, 肖燕妮, 徐宗本 2020 中国科学: 数学 48 0037
Google Scholar
Wang X, Tang S Y, Chen Y, Feng X M, Xiao Y N, Xu Z B 2020 Sci. Sin. Math. 48 0037
Google Scholar
[31] 张彦平 2020 中华流行病学杂志 41 145
Google Scholar
Zhang Y P 2020 Chin. J. Epidemiol. 41 145
Google Scholar
[32] Zhu X L, Zhang A Y, Xu S, Jia P F, Tan X Y, Tian J Q, Wei T, Quan Z X, Yu J L 2020 medRxiv: 02.09.20021360 v1
[33] Shen M W, Peng Z H, Xiao Y N, Zhang L 2020 bioRxiv: 01.23.916726 v1
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