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浙江大学学报(医学版)  2021, Vol. 50 Issue (1): 68-73    DOI: 10.3724/zdxbyxb-2021-0043
2019冠状病毒病     
利用人口流动数据以及两阶段模型预测2019冠状病毒病流行趋势
叶元庆1,2,3(),雷浩1,2,陈辰1,2,胡可嘉1,2,徐小林1,2,袁长征1,2,曹淑殷1,2,王思思1,2,王思聪1,2,李舒1,2,应智峻1,2,贾君麟1,2,王秦川2,4,Sten H.VERMUND5,许正平6,7,*(),吴息凤1,2,3
1. 浙江大学医学院附属第二医院生物统计、生物信息学和大数据中心,浙江 杭州 310009
2. 浙江大学医学院公共卫生学院大数据健康科学系,浙江 杭州 310058
3. 浙江大学健康医疗大数据国家研究院,浙江 杭州 310058
4. 浙江大学医学院附属邵逸夫医院肿瘤外科,浙江 杭州 310016
5. 美国耶鲁大学耶鲁公共卫生学院,康涅狄格州 纽黑文市 06520
6. 浙江大学医学院环境医学研究所,浙江 杭州 310058
7. 浙江大学感染性疾病诊治协同创新中心,浙江 杭州 310003
Predicting COVID-19 epidemiological trend by applying population mobility data in two-stage modeling
YE Yuanqing1,2,3(),LEI Hao1,2,CHEN Chen1,2,HU Kejia1,2,XU Xiaolin1,2,YUAN Changzheng1,2,CAO Shuyin1,2,WANG Sisi1,2,WANG Sicong1,2,LI Shu1,2,YING Zhijun1,2,JIA Junlin1,2,WANG Qinchuan2,4,Sten H. VERMUND5,XU Zhengping6,7,*(),WU Xifeng1,2,3
1. Center for Biostatistics,Bioinformatics and Big Data,the Second Affiliated Hospital,Zhejiang University School of Medicine,Hangzhou 310009,China;
2. Department of Big Data in Health Science,School of Public Health,Zhejiang University School of Medicine,Hangzhou 310058,China;
3. National Institute for Data Science in Health and Medicine,Zhejiang University,Hangzhou 310058,China;
4. Department of Surgical Oncology,Sir Run Run Shaw Hospital,Zhejiang University School of Medicine,Hangzhou 310016,China;
5. Yale School of Public Health,Yale University,New Haven 06520,Connecticut,USA;
6. Institute of Environmental Medicine,Zhejiang University School of Medicine,Hangzhou 310058,China;
7. Collaborative Innovation Center for Diagnosis and Treatment of Infectious Diseases,Zhejiang University,Hangzhou 310003,China
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摘要:

目的:基于人口流动和疫情防控措施信息构建数学模型,预测2019冠状病毒病(COVID-19)疫情的发展趋势。 方法:获取截至2020年2月8日浙江省乐清市151例确诊病例的患病过程以及乐清和武汉之间的人口流动等信息,采用两阶段的方法构建数学模型,将人口流动数据与确诊病例症状开始时间以及输入性病例和本地病例的传播动力学特征整合起来,模拟并预测乐清的COVID-19疫情发展趋势。 结果:在疫情初期,每日从武汉来的输入性病例数(症状出现日)与当日、 6?d前和 9?d前从武汉到乐清的旅客数量成正相关。利用根据武汉到乐清的旅客数量估计的输入性病例数以及易感-暴露-感染-恢复模型预测乐清最终的病例数为170例。如果根据每日报告的输入性病例数来预测,预计最终病例数为165例。截至2020年4月27日,乐清实际监测到的病例数为170例,这两个预测值与实际值均接近。 结论:本研究建立的两阶段预测模型能够对COVID-19的流行趋势做出准确预测。

关键词: 2019冠状病毒病;中国输入病例本地病例易感-暴露-感染-恢复模型预测    
Abstract:

Objective:To predict the epidemiological trend of coronavirus disease 2019 (COVID-19) by mathematical modeling based on the population mobility and the epidemic prevention and control measures. Methods: As of February 8,2020,the information of 151 confirmed cases in Yueqing,Zhejiang province were obtained,including patients’ infection process,population mobility between Yueqing and Wuhan,etc. To simulate and predict the development trend of COVID-19 in Yueqing, the study established two-stage mathematical models,integrating the population mobility data with the date of symptom appearance of confirmed cases and the transmission dynamics of imported and local cases. Results: It was found that in the early stage of the pandemic,the number of daily imported cases from Wuhan (using the date of symptom appearance) was positively associated with the number of population travelling from Wuhan to Yueqing on the same day and 6 and 9 days before that. The study predicted that the final outbreak size in Yueqing would be 170 according to the number of imported cases estimated by consulting the population number travelling from Wuhan to Yueqing and the susceptible-exposed-infectious-recovered (SEIR) model; while the number would be 165 if using the reported daily number of imported cases. These estimates were close to the 170,the actual monitoring number of cases in Yueqing as of April 27,2020. Conclusion: The two-stage modeling approach used in this study can accurately predict COVID-19 epidemiological trend.

Key words: Coronavirus disease 2019; China    Imported cases    Indigenous cases    Susceptible-exposed-infectious-recovered model    Prediction
收稿日期: 2020-10-19 出版日期: 2021-05-16
CLC:  R181.2  
基金资助: 浙江大学新型冠状病毒(2019-nCoV)肺炎应急科研专项(2020XGZX003);浙江省创新团队(2019R01007);浙江省重点实验室(2020E10004);浙江省自然科学基金(LEZ20H260002)
通讯作者: 许正平     E-mail: yuanqing99@zju.edu.cn;zpxu@zju.edu.cn
作者简介: 叶元庆,研究员,博士生导师,主要从事遗传流行病学研究;E-mail:yuanqing99@zju.edu.cn;https://orcid.org/0000-0001-5708-8961. 雷浩,讲师,主要从事传染病流行病学研究;E-mail:leolei@zju.edu.cn;https://orcid.org/0000-0002-1850-7040
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引用本文:

叶元庆,雷浩,陈辰,胡可嘉,徐小林,袁长征,曹淑殷,王思思,王思聪,李舒,应智峻,贾君麟,王秦川,Sten H.VERMUND,许正平,吴息凤. 利用人口流动数据以及两阶段模型预测2019冠状病毒病流行趋势[J]. 浙江大学学报(医学版), 2021, 50(1): 68-73.

YE Yuanqing,LEI Hao,CHEN Chen,HU Kejia,XU Xiaolin,YUAN Changzheng,CAO Shuyin,WANG Sisi,WANG Sicong,LI Shu,YING Zhijun,JIA Junlin,WANG Qinchuan,Sten H. VERMUND,XU Zhengping,WU Xifeng. Predicting COVID-19 epidemiological trend by applying population mobility data in two-stage modeling. J Zhejiang Univ (Med Sci), 2021, 50(1): 68-73.

链接本文:

http://www.zjujournals.com/med/CN/10.3724/zdxbyxb-2021-0043        http://www.zjujournals.com/med/CN/Y2021/V50/I1/68

f ( t ) = γ 0 + γ t + i = 0 10 α i w t ? i + i = 0 10 β i w t ? i × t (1)
  
w t ? i = ε 2 w t ? i ' / ε 1 (2)
  
S ( t + 1 ) = S ( t ) ? β ( t ) [ I ( t ) + E ( t ) + I i n ( t ) ] S ( t ) N (3)
  
E ( t + 1 ) = E ( t ) + β ( t ) [ I ( t ) + E ( t ) + I i n ( t ) ] S ( t ) N ? E ( t ) k
  
I ( t + 1 ) = I ( t ) + E ( t ) k ? I ( t ) D + k (5)
  
R ( t + 1 ) = R ( t ) + I ( t ) D + k (6)
  
f ( t ) = ? 0.13 ?t ? 0.41 ? w t + 0.10 w t × t + 0.13 w ( t ? 6 ) + 0.01 w ( t ? 6 ) × t ? 1.96 w ( t ? 9 ) + 0.08 w ( t ? 9 ) × t + 4.33 (7)
  
图 1  2020年1月8日至2月8日乐清市每日2019冠状病毒病输入病例数及本地病例数
图 2  模型预测2020年1月8日至2月8日乐清市每日2019冠状病毒病输入病例数
图 3  模拟和实际报道乐清每日新增和累计确诊2019冠状病毒病病例数 A、B:基于公预测的每日输入病例数预测;C、D:基于每日实际输入病例数预测.平滑后的本地病例指根据平滑而得到的.
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