乌鲁木齐市COVID-19传播的动力学模型研究

廖影; 张学良; 焦海燕; 王蕾

doi:10.16462/j.cnki.zhjbkz.2021.08.007

乌鲁木齐市COVID-19传播的动力学模型研究

doi: 10.16462/j.cnki.zhjbkz.2021.08.007

廖影¹,
张学良²,
焦海燕¹,
王蕾^2, ,

1.
830011 乌鲁木齐，新疆医科大学公共卫生学院流行病与卫生统计学教研室
2.
830011 乌鲁木齐，新疆医科大学医学工程技术学院数学教研室

基金项目:

国家自然科学基金 12061079

新疆维吾尔自治区自然科学基金 2021D01C268

新疆维吾尔自治区自然科学基金 2019D01C206

详细信息

通讯作者:
王蕾，E-mail: wlei81@126.com

中图分类号: R181
计量
- 文章访问数: 425
- HTML全文浏览量: 218
- PDF下载量: 90
- 被引次数: 0
出版历程
- 收稿日期: 2021-02-07
- 修回日期: 2021-03-22
- 网络出版日期: 2021-08-24
- 刊出日期: 2021-08-10

A dynamical model study on the transmission of COVID-19 in Urumqi City

1.
Department of Epidemiology and Health Statistics, College of Public Health, Xinjiang Medical University, Urumqi 830011, China
2.
Department of Math, College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830011, China

Funds:

National Natural Science Foundation of China 12061079

Natural Science Foundation of Xinjiang Uygur Autonomous Region 2021D01C268

Natural Science Foundation of Xinjiang Uygur Autonomous Region 2019D01C206

More Information

Corresponding author: WANG Lei, E-mail: wlei81@126.com

摘要

摘要: 目的拟合新疆维吾尔自治区乌鲁木齐市2020年7月COVID-19疫情流行状况，为疫情防控提供数量依据和理论支撑。方法利用仓室建模方法，考虑乌鲁木齐市在2020年7月COVID-19疫情期间所采取的追踪隔离措施，建立具有阶段性控制策略的动力学模型。利用新疆维吾尔自治区卫生健康委员会公布的2020年7-9月COVID-19的累计确诊病例数、累计治愈病例数、累计无症状病例数，使用非线性最小二乘法拟合所建立的模型。结果模型的参数估计：确诊速率为0.6，潜伏暴露者类和无症状感染者类的传染力系数分别为0.78和0.99，无症状感染者所占比例为0.4。参数敏感性分析表明，加大密切追踪隔离力度和减少接触能有效控制新增确诊病例。结论所建立的模型拟合实际数据效果较好；无症状感染者传染性较强；每日有效再生数变化趋势表明政府控制措施得当，控制效果较好；相关部门应加大密切追踪隔离力度、持续强调减少接触可以有效控制COVID-19的流行。
- COVID-19 /
- 无症状感染者 /
- 多源数据 /
- 控制策略 /
- 有效再生数
Abstract: Objective To fit the epidemic situation of COVID-19 in Urumqi City, Xinjiang Uygur Autonomous Region in July 2020, so as to provide the quantitative and theoretical basis for the prevention and control of epidemic. Methods A dynamical model with stage control strategy was proposed using compartmental modeling method, based on the tracking and isolation measures taken during the COVID-19 epidemic in July 2020 in Urumqi City. The nonlinear least square method was applied to fit this dynamical model by using multi-source data: the cumulative number of confirmed cases, cured cases and asymptomatic cases of COVID-19 from Health Committee of Xinjiang from July to September 2020. Results The parameters of the model were estimated as follows: the rate of diagnosis was 0.6, the infectivity coefficients of latent exposure group and asymptomatic infection group were 0.78 and 0.99 respectively, and the proportion of asymptomatic infection group was 0.4. Parameter sensitivity analysis showed that increasing close tracking and isolation and reducing contact could effectively control the number of new confirmed cases. Conclusion The results show that the model has good fitting effect with the actual data; asymptomatic infection is more infectious; the trend of daily effective reproduction number shows that the government control measures are appropriate with great effect; the relevant departments should increase the close tracking and isolation, and continuously emphasize that reducing contact can effectively control the epidemic of COVID-19.
- COVID-19 /
- Asymptomatical cases /
- Multiple source data /
- Control strategy /
- Effective reproduction number

HTML全文

图 1 2020年7-9月乌鲁木齐市考虑隔离措施和无症状感染者类的COVID-19传播流程

Figure 1. Flow chart of COVID-19 transmission considering isolation measures and asymptomatic cases in Urumqi City from July to September 2020

下载: 全尺寸图片幻灯片

图 2 2020年7-9月COVID-19乌鲁木齐市累计确诊(A)、累计治愈(B)、累计无症状病例数(C)与模型(1)的拟合图

Figure 2. Fitting diagram of cumulative number of confirmed cases(A)、cumulative number of cured cases(B) and cumulative number of asymptomatic cases(C) of COVID-19 in Urumqi City in July to September 2020 with model (1)

下载: 全尺寸图片幻灯片

图 3 参数的偏相关系数值[(A)10 000次、(B)12 000次)]

注：^a表示影响有统计学意义的参数。

Figure 3. Partial rank correlation coefficient values of parameters [(A)10 000 times、(B)12 000 times)]

下载: 全尺寸图片幻灯片

图 4 参数q、σ、c₀、β和ε对COVID-19新增确诊病例数的影响

Figure 4. The influence of parameters q, σ, c₀, β and ε on the number of new confirmed cases of COVID-19

下载: 全尺寸图片幻灯片

表 1 模型参数估计及其含义

Table 1. Model parameter estimation and its meaning

参数	含义	值	来源
S(0)	初始S人数	37 000	参数估计
E(0)	初始E人数	26(25.11)	参数估计
I(0)	初始I人数	12(11.328)	参数估计
A(0)	初始A人数	4(3.4)	参数估计
R(0)	初始R人数	0	已有研究^[8]
H(0)	初始H人数	0	已有研究^[8]
Sq(0)	初始Sq(无被传染风险)	0	已有研究^[8]
B(0)	初始B人数	0	已有研究^[8]
q	接触者隔离率	0.33	参数估计
β	每次接触传播概率	0.07	参数估计
c₀	疾病暴发早期接触数	18.00	参数估计
cb	防控策略实施后的最小接触数	2.00	参数估计
r1	接触数的指数下降率	0.24	参数估计
m	通过发热门诊进入B的隔离率	0.07	参数估计
b	B检测率	5.5×10^-15	参数估计
f	疑似病例的检出率	0.91	参数估计
ε	E传染力系数	0.78	参数估计
θ	A传染力系数	0.99	参数估计
λ	解除隔离率	1/14	已有研究^[3]
γA	A移出速率	0.10	已有研究^[12]
γI	I移出速率	0.10	已有研究^[12]
γH	H移出速率	0.10	已有研究^[12]
δA	从A到H的确诊速率	0.60	参数估计
δI	从I到H的确诊速率	0.60	参数估计
d	因病死亡率	0.019	参数估计
η	I占感染者的比例	0.60	参数估计
σ	E进展为感染者的速率(潜伏期的倒数)	1/7	已有研究^[3]

下载: 导出CSV

表 2 MAPE和RMSPE评价结果

Table 2. Evaluation results of MAPE and RMSPE

比较对象	MAPE(RMSPE) (%)	拟合结果
实际确诊与拟合确诊	8.36(23.39)	精准(合理)
实际治愈与拟合治愈	17.13(41.70)	较好(合理)
实际无症状与拟合无症状	3.16(9.57)	精准(精准)

下载: 导出CSV

参考文献(13)

[1]	中华人民共和国国家卫生健康委员会. 新型冠状病毒肺炎诊疗方案(试行第八版)[J]. 中华临床感染病杂志, 2020, 13(5): 321-328. DOI: 10.3760/cma.j.issn.1674-2397.2020.05.001. National Health Commission of the People's Republic of China. COVID-19 diagnosis and treatment plan (trial eighth edition)[J]. Chin J Clin Infect Dis, 2020, 13(5): 321-328. DOI: 10.3760/cma.j.issn.1674-2397.2020.05.001.
[2]	白宁, 宋晨玮, 徐瑞. 基于动力学模型的COVID-19疫情预测与控制策略研究[J]. 应用数学学报, 2020, 43(3): 483-493. https://www.cnki.com.cn/Article/CJFDTOTAL-YYSU202003001.htm Bai N, Song CW, Xu R. Predicting the trend and evaluating control strategies of COVID-19 based on a dynamical model[J]. Acta Math Appl Sin, 2020, 43(3): 483-493 https://www.cnki.com.cn/Article/CJFDTOTAL-YYSU202003001.htm
[3]	Tang B, Wang X, Li Q, et al. Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions[J]. J Clin Med, 2020, 9(2): E462. DOI: 10.3390/jcm9020462.
[4]	Tang B, Bragazzi NL, Li Q, et al. An updated estimation of the risk of transmission of the novel coronavirus (2019-nCoV)[J]. Infect Dis Model, 2020, 5: 248-255. DOI: 10.1016/j.idm.2020.02.001.
[5]	Feng XM, Chen J, Wang K, et al. Phase-adjusted estimation of the COVID-19 outbreak in South Korea under multi-source data and adjustment measures: a modelling study[J]. Math Biosci Eng, 2020, 17(4): 3637-3648. DOI: 10.3934/mbe.2020205.
[6]	俞骅, 王旭初, 李钧, 等. 杭州市首例新型冠状病毒肺炎病例病毒全基因组序列测定及分析[J]. 中华预防医学杂志, 2020, 54(5): 486-490. DOI: 10.3760/cma.j.cn112150-20200217-00128. Yu H, Wang XC, Li J, et al. Genomic analysis of a 2019-novel coronavirus (2019-nCoV) strain in the first COVID-19 patient found in Hangzhou[J]. Chin J Prev Med, 2020, 54(5): 486-490. DOI: 10.3760/cma.j.cn112150-20200217-00128.
[7]	朱正保, 仲崇科, 张凯欣, 等. 中国内地新型冠状病毒肺炎流行趋势分析[J]. 中华预防医学杂志, 2020, 54(6): 620-624. DOI: 10.3760/cma.j.cn112150-20200222-00163. Zhu ZB, Zhong CK, Zhang KX, et al. Epidemic trend of COVID-19 in Chinese mainland[J]. Chin J Prev Med, 2020, 54(6): 620-624. DOI: 10.3760/cma.j.cn112150-20200222-00163.
[8]	新疆维吾尔自治区卫生健康委员会. 防控新型冠状病毒肺炎疫情[EB/OL]. (2020-07-15)[2020-09-17]. http://wjw.xinjiang.gov.cn/hfpc/fkxxfy/fkxxfy.shtml. Health Committee of Xinjiang Uygur Autonomous Region. Prevention and control of new coronavirus pneumonia[EB/OL]. (2020-07-15)[2020-09-17]. http://wjw.xinjiang.gov.cn/hfpc/fkxxfy/fkxxfy.shtml.
[9]	马知恩, 周义仓, 李建全, 等. 传染病动力学的数学建模与研究[M]. 北京: 科学出版社, 2004: 1-20. Ma ZE, Zhou YC, Li JQ, et al. Mathematical modeling and research on dynamics of infectious diseases[M]. Beijing: Science Press, 2004: 1-20.
[10]	Wang WD, Zhao XQ. Threshold dynamics for compartmental epidemic models in periodic environments[J]. J Dyn Differ Equations, 2008, 20(3): 699-717. DOI: 10.1007/s10884-008-9111-8.
[11]	乌鲁木齐市人民政府乌鲁木齐市统计局. 2019年乌鲁木齐市国民经济和社会发展统计公报[EB/OL]. (2020-06-18)[2020-06-18]. http://www.urumqi.gov.cn/fjbm/tjj/tjgb/446900.htm. Urumqi Statistics Bureau of Urumqi Municipal People's Government. Statistical bulletin of national economic and social development of Urumqi in 2019[EB/OL]. (2020-06-18)[2020-06-18]. http://www.urumqi.gov.cn/fjbm/tjj/tjgb/446900.htm.
[12]	魏永越, 卢珍珍, 杜志成, 等. 基于改进的SEIR+CAQ传染病动力学模型进行新型冠状病毒肺炎疫情趋势分析[J]. 中华流行病学杂志, 2020, 41(4): 470-474, 475. DOI: 10.3760/cma.j.cn112338-20200216-00106. Wei YY, Lu ZZ, Du ZC, et al. Fitting and forecasting the trend of COVID-19 by SEIR+CAQ dynamic model[J]. Chin J Epidemiol, 2020, 41(4): 470-474, 475. DOI: 10.3760/cma.j.cn112338-20200216-00106.
[13]	唐三一, 唐彪, Nicola Luigi Bragazzi, 等. 新型冠状病毒肺炎疫情数据挖掘与离散随机传播动力学模型分析[J]. 中国科学: 数学, 2020, 50(8): 1071-1086. DOI: 10.1360/SSM-2020-0053. Tang SY, Tang B, Bragazzi N, et al. Analysis of COVID-19 epidemic traced data and stochastic discrete transmission dynamic model[J]. Sci Sin Math, 2020, 50(8): 1071-1086. DOI: 10.1360/SSM-2020-0053.