Epidemiological parameters and models of coronavirus disease 2019

Ying-Ke Li; Shi Zhao; Yi-Jun Lou; Dao-Zhou Gao; Lin Yang; Dai-Hai He

doi:10.7498/aps.69.20200389

Journals >Acta Physica Sinica >Volume 69 >Issue 9 >Page 090202-1 > Article

Acta Physica Sinica
Vol. 69, Issue 9, 090202-1 (2020)

Epidemiological parameters and models of coronavirus disease 2019

Ying-Ke Li^1、*, Shi Zhao², Yi-Jun Lou³, Dao-Zhou Gao⁴, Lin Yang⁵, and Dai-Hai He^3、*

Author Affiliations

¹College of Mathematics and Physics, Xinjiang Agriculture University, Urumqi 830052, China

²JC School of Public Health and Primary Care, The Chinese University of Hong Kong, Hong Kong 999077, China

³Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong 999077, China

⁴Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

⁵School of Nursing, Hong Kong Polytechnic University, Hong Kong 999077, China

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DOI: 10.7498/aps.69.20200389 Cite this Article

Ying-Ke Li, Shi Zhao, Yi-Jun Lou, Dao-Zhou Gao, Lin Yang, Dai-Hai He. Epidemiological parameters and models of coronavirus disease 2019[J]. Acta Physica Sinica, 2020, 69(9): 090202-1 Copy Citation Text

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Fig. 1. (a) Daily new cases simulated versus reporting; (b) daily reporting rate

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Fig. 2. Curves of daily confirmed cases and instantaneous reproductive number of the top 20 countries with the most cumulative cases

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Fig. 3. Curves of daily confirmed cases and instantaneous reproductive number of the 21st − 40th countries with the most cumulative cases.

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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	${\cal{R} }_{0}=\dfrac{r}{\displaystyle\sum\limits_{i=1}^{n}y_i\dfrac{ {\rm e }^{-ra_{i-1} }-{\rm e}^{-ra_i} }{a_i-a_{i-1} } }$	a_i与 $y_i$分别表示年龄与相应频率

Table 1. The formula of the basic reproduction number

under different models or distributions.

地点	${\cal{R}}_0$	置信区间	截止时间	计算方法	参考文献
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.
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]

Table 2. Summary of the basic reproduction number

for COVID-19.

点估计	置信区间	分布形式	截止时间	估计方法	参考文献
注: M: n表示均值是n天, Me: n表示中位数是n天. 表4含义表示相同.
M: 5.2	[4.1, 7.0]	指数增长	2020/01/22	—	[1]
M: 6.4	[5.6, 7.7]	威布尔	2020/01/29	贝叶斯	[6]
M: 5.0	[4.2, 6.0]	对数正态	2020/01/23	最优化	[7]
Me: 5.2	[4.4, 6.0]	对数正态	2020/01/30	最优化	[7]
Me: 4.0	—	经验分布	2020/01/29	非参数估计	[11]

Table 3. Summary of the incubation period for COVID-19.

时间/d	置信区间	截止时间	估计方法	参考文献
M: 7.5	[5.3, 19.0]	2020/01	最优化	[1]
M: 4.41	—	2020/02/02	最优化	[24]
M: 4.7	[3.7, 6.0]	2020/02	最优化	[25]

Table 4. Summary of the serial interval for COVID-19.

Ying-Ke Li, Shi Zhao, Yi-Jun Lou, Dao-Zhou Gao, Lin Yang, Dai-Hai He. Epidemiological parameters and models of coronavirus disease 2019[J]. Acta Physica Sinica, 2020, 69(9): 090202-1

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