基于再生数的上海市奥密克戎流行趋势研究

王子涵; 徐梦霞; 方立群; 张勇

doi:10.16462/j.cnki.zhjbkz.2024.03.013

基于再生数的上海市奥密克戎流行趋势研究

doi: 10.16462/j.cnki.zhjbkz.2024.03.013

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

基金项目:

国家自然科学基金 11501035

详细信息

通讯作者:
张勇，E-mail：zhangyong@bnu.edu.cn

中图分类号: R181
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- 被引次数: 0
出版历程
- 收稿日期: 2022-06-07
- 修回日期: 2022-09-24
- 网络出版日期: 2024-04-08
- 刊出日期: 2024-03-10

Study on the epidemic trend of Omicron in Shanghai based on the reproduction number

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

Funds:

National Natural Science Foundation of China 11501035

More Information

Corresponding author: ZHANG Yong, E-mail: zhangyong@bnu.edu.cn

摘要

摘要: 目的基于截至2022年5月9日上海市奥密克戎(Omicron)的流行趋势，估计封控管理之前的早期再生数(R)以及后续的有效再生数(R_t)变化情况。方法利用指数增长法、最大似然法和下一代矩阵法估计R，利用贝叶斯方法、时依法和新时变法估计R_t。结果截至2022年3月29日上海市奥密克戎疫情呈指数增长模式。3种方法估计的R值分别为2.36(95% CI：2.33~2.38)，2.14(95% CI：2.11~2.18)和2.29(95% CI：2.22~2.38)。结论 R值较大，上海市早期疫情形势较为严峻。自4月7日起，R_t呈下降趋势，表明封控管理措施有效地减缓了疫情增长。R_t的计算方法中，时依法和新时变法可以较快地响应疫情的动态变化趋势；而贝叶斯法反应较为迟缓，且当报告数据波动较大时，会出现分母为0导致无法计算的情况。
- COVID-19 /
- 奥密克戎 /
- 再生数
Abstract: Objective To study the epidemic trend of Omicron in Shanghai as of May 9, 2022 by estimating the early reproduction number (R) before closed management and the subsequent changes of effective reproduction number (R_t). Methods Exponential growth method, maximum likelihood method and next generation matrix method were used to estimate R, and Bayesian method, Time-Dependent and New Time-Varying were used to estimate R_t. Results As of March 29, 2022, the growth of Omicron epidemic in Shanghai followed the exponential growth. The early reproduction number R estimated by three methods was 2.36(95% CI: 2.33-2.38), 2.14(95% CI: 2.11-2.18) and 2.29(95% CI: 2.22-2.38), respectively. Conclusion s As the values of R were relatively large, the early epidemic situation in Shanghai was severe. The turning point of the epidemic was on April 7, and the implementation of sealing and control management measures had effectively slowed down the increment of the epidemic cases. Among the methods for calculating the R_t, the Time-Dependent and New Time-Varying can quickly respond to the dynamic trend of the epidemic, while the Bayesian method was relatively slow. Besides, when the reported data fluctuated greatly, the denominator would be zero, thus R_t would be unable to calculate.
- COVID-19 /
- Omicron /
- Reproduction number

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图 1 每日新增确诊病例和无症状病例数

Figure 1. Number of newly confirmed cases and asymptomatic cases

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图 2 2022年3月1日―4月13日指数增长拟合的RNew值

Figure 2. RNew value of exponential growth fitting from March 1 to April 13, 2022

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图 3 指数增长曲线拟合2022年3月1―29日累计感染病例数

Figure 3. Exponential growth curve fitting cumulative number of infected cases from March 1 to March 29, 2022

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图 4 SEAIR模型中人群转化关系图

S: 易感者仓室; E: 暴露者仓室; A: 无症状者仓室; I: 确诊者仓室; R: 移出者仓室。

Figure 4. The transformation relationship diagram of the SEAIR model

S: compartment of susceptible individuals; E: compartment of exposed individuals; A: compartment of asymptomatic individuals; I: compartment of infective individuals; R: compartment of removed individuals.

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图 5 SEAIR模型累计病例数拟合结果

Figure 5. Fitting results of cumulative cases of SEAIR model

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图 6 3月1日起100 d各仓室中人数预测

S, 易感者仓室; E, 暴露者仓室; A, 无症状者仓室; I, 确诊者仓室; R, 移出者仓室。

Figure 6. Forecast of the number of people in each compartment in 100 days from March 1

S, compartment of susceptible individuals; E, compartment of exposed individuals; A, compartment of asymptomatic individuals; I, compartment of infective individuals; R, compartment of removed individuals.

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图 7 贝叶斯法估计有效再生数

Figure 7. Estimation of effective reproduction number by Bayesian method

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图 8 时依法估计有效再生数

Figure 8. Estimation of effective reproduction number by Time-Dependent method

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图 9 新时变法估计有效再生数

Figure 9. Estimation of effective reproduction number by New Time-Varying method

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图 10 贝叶斯方法中R_t的分布变化

Figure 10. The change of distribution of R_t in Bayesian method

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表 1 SEAIR模型中各参数及意义

Table 1. Significance of parameters in SEAIR model

参数Parameter	意义Significance
β	有效接触率 Contact rate
γ	潜伏期的倒数 Reciprocal of incubation period
σ	被感染后无症状的比例 Proportion of asymptomatic cases
θ	无症状感染者的传染率 Infection rate of asymptomatic cases
α_A	无症状感染者的康复率 Recovery rate of asymptomatic cases
α_I	确诊患者的康复率 Recovery rate of confirmed cases

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表 2 SEAIR仓室模型中各参数取值

Table 2. Values of parameters in SEAIR compartment model

参数Parameter	取值Value
θ	0.40
α_A	0.33
σ	0.96
β	1.60
γ	2.20
α_I	0.14

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表 3 The early reproduction number in Shanghai (3.1-3.29)

计算方法 Computation method	早期再生数估计值(95% CI) Estimated value of early reproduction number (95% CI)
指数增长法 Exponential growth method	2.36(2.33~2.38)
最大似然法 Maximum likelihood method	2.14(2.11~2.18)
下一代矩阵法 Next generation matrix method	2.29(2.22~2.38)

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表 4 2020年COVID-19与2022年奥密克戎再生数对比

Table 4. Comparison between the reproduction numbers of COVID-19 in 2020 and Omicron in 2022

计算方法 Method of calculation	2020年2月COVID-19早期再生数 Early reproduction number of COVID-9 in February 2020	2022年3月奥密克戎早期再生数 Early reproduction number of Omicron in March 2022
指数增长法Exponential growth method	3.74(3.63~2.87)	2.36(2.33~2.38)
最大似然法Maximum likelihood method	3.16(2.90~3.43)	2.14(2.11~2.18)
下一代矩阵法Next generation matrix method	3.91(3.71~4.11)	2.29(2.22~2.38)

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