﻿ 新型冠状病毒肺炎的早期传染病流行病学参数估计研究
 中华流行病学杂志  2020, Vol. 41 Issue (4): 461-465 PDF
http://dx.doi.org/10.3760/cma.j.cn112338-20200205-00069

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#### 文章信息

Song Qianqian, Zhao Han, Fang Liqun, Liu Wei, Zheng Chuang, Zhang Yong

Study on assessing early epidemiological parameters of COVID-19 epidemic in China

Chinese Journal of Epidemiology, 2020, 41(4): 461-465
http://dx.doi.org/10.3760/cma.j.cn112338-20200205-00069

### 文章历史

1. 北京师范大学数学科学学院 100875;
2. 军事医学研究院微生物流行病研究所, 北京 100071

Study on assessing early epidemiological parameters of COVID-19 epidemic in China
Song Qianqian1 , Zhao Han1 , Fang Liqun2 , Liu Wei2 , Zheng Chuang1 , Zhang Yong1
1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;
2. Institute of Microbiology and Epidemiology, Academy of Military Medical Sciences, Beijing 100071, China
Abstract: Objective To study the early dynamics of the epidemic of coronavirus disease (COVID-19) in China from 15 to 31 January, 2020, and estimate the corresponding epidemiological parameters (incubation period, generation interval and basic reproduction number) of the epidemic. Methods By means of Weibull, Gamma and Lognormal distributions methods, we estimated the probability distribution of the incubation period and generation interval data obtained from the reported COVID-19 cases. Moreover, the AIC criterion was used to determine the optimal distribution. Considering the epidemic is ongoing, the exponential growth model was used to fit the incidence data of COVID-19 from 10 to 31 January, 2020, and exponential growth method, maximum likelihood method and SEIR model were used to estimate the basic reproduction number. Results Early COVID-19 cases kept an increase in exponential growth manner before 26 January, 2020, then the increase trend became slower. The average incubation period was 5.01 (95%CI:4.31-5.69) days; the average generation interval was 6.03 (95%CI:5.20-6.91) days. The basic reproduction number was estimated to be 3.74 (95%CI:3.63-3.87), 3.16 (95%CI:2.90-3.43), and 3.91 (95%CI:3.71-4.11) by three methods, respectively. Conclusions The Gamma distribution fits both the generation interval and incubation period best, and the mean value of generation interval is 1.02 day longer than that of incubation period. The relatively high basic reproduction number indicates that the epidemic is still serious; Based on our analysis, the turning point of the epidemic would be seen on 26 January, the growth rate would be lower afterwards.
Key words: COVID-19    Incubation period    Generation interval    Basic reproduction number

2019年12月31日，湖北省武汉市暴发原因不明的肺炎，随后WHO确认这是由一种新型冠状病毒引起的。自2019年12月12日以来，武汉市卫生健康委员会报告了27例新型冠状病毒肺炎（COVID-19）病例，其中7例为重症病例。截至2020年1月31日24：00，中国内地共报告COVID-19确诊病例11 791例[1]。COVID-19传播途径主要是经呼吸道飞沫传播，目前大多数病例与密切接触有关，并且人群普遍易感。

1.数据来源：病例数据源于国家和各省份卫生健康委员会每日更新的日累计病例数及相关网站报告的病例和密切接触人群等信息，截至2020年1月31日，全国报告确诊病例为11 791例。收集的信息包括报告病例的累计数，每日新增病例数，已解除医学观察人员累计数（图 1）。其中2020年1月1－15日每天报告的累计病例数均为41例，期间无新增病例。

 图 1 2020年1月全国新型冠状病毒感染情况

2.潜伏期和世代间隔估计：潜伏期为一个感染者的被感染时间与其出现临床症状的时间之差[6]，世代间隔指一个感染者的被感染时间与其下一代感染者的被感染时间之差[7]。潜伏期的估计至关重要，是确定暴露人员隔离期限和判断病例感染时间的重要依据，同时也是流行病学预测模型的关键参数；世代间隔代表了疾病从一个人传至另一个人的平均间隔时间，世代间隔时间越短疫情越容易呈现暴发模式。部分病例接触传染源的时间不能直接观察到，这导致对潜伏期的估计较为困难。通常我们不能精确地观察到暴露于传染源和症状出现的时间，它们可能落入某些间隔。但可通过确定每个病例暴露的最早和最晚时间以及出现症状时间之差估计潜伏期，将此时间视为每个人潜伏期的区间截断估计值[8]

R0是流行病模型中的一个重要参数，表示在发病初期，当所有人均为易感者时，一名病例在其患病期内所传染的平均人数。当R0＞1时，流行病会暴发；否则疫情将会结束。

（1）定义r为累计感染病例数的指数增长率，Ct）为COVID-19的累计病例数。在初始阶段，累计病例数往往呈指数增长，但这个指数增长阶段到底会持续多久就需要人们进行判定。本研究采用拟合优度系数R2的大小判断初始指数增长阶段的持续时间长度。由于病例数是整数值，因此采用泊松回归估计该参数[14]。参照文献[13]计算R0

（2）假设二代病例服从期望值为R0的泊松分布，令N0N1，…，NT表示连续单位时间内的病例数，世代间隔用ω表示，则R0可以由最大化对数似然估计函数估出[15]

（3）应用经典的传染病SEIR仓室模型分析中国COVID-19的传播动态。需要强调：SEIR数学模型中的暴露人群[Et）]是指暴露但不具有传染性的人群。由于该疾病潜伏期后期可能具有传染性[16]，故模型中将具有传染性的潜伏期病例归为感染类I，暴露类E为无传染性的暴露人员，从而疫情传播动态可以使用以下微分方程组描述：

 注：A：柱状图为90个病例潜伏期的频率分布；B：使用威布尔、伽马和对数正态分布模型估计的累计分布曲线与病例数据曲线进行比较；C：1 000次Bootstrap重采样数据拟合的潜伏期伽马分布（仅显示了300次样数据拟合值与平均值） 图 2 COVID-19潜伏期拟合结果
 注：A：柱状图为35个病例世代间隔的频率分布；B：使用威布尔、伽马和对数正态分布模型估计的累计分布曲线与病例数据曲线进行比较；C：1 000次Bootstrap重采样数据拟合的世代间隔伽马分布（仅显示了300次样数据拟合值与平均值） 图 3 世代间隔拟合COVID-19结果

 图 4 COVID-19初始指数增长阶段R2系数
 图 5 指数增长曲线拟合2020年1月COVID-19累计病例数
 图 6 SEIR模型拟合2020年1月COVID-19图

3种方法计算出的R0值都明显＞1，平均为3.60，高于SARS（R0＝2.7）[24]和MERS（R0＝2.0~2.8）[25]。这意味着COVID-19疫情还处于暴发期，形势较为严峻。

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