Please wait a minute...
浙江大学学报（医学版）
J Zhejiang Univ (Med Sci)  2020, Vol. 49 Issue (2): 178-184    DOI: 10.3785/j.issn.1008-9292.2020.02.05
    
Study on the epidemic development of COVID-19 in Hubei province by a modified SEIR model
CAO Shengli1(),FENG Peihua2(),SHI Pengpeng3,*()
1. School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an 710049, China
2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China
3. School of Civil Engineering&Institute of Mechanics and Technology, Xi'an University of Architecture and Technology, Xi'an 710055, China
Download: HTML( 424 )   PDF(2555KB)
Export: BibTeX | EndNote (RIS)      

Abstract  

Objective: To establish a SEIR epidemic dynamics model that can be used to evaluate the COVID-19 epidemic, and to predict and evaluate the COVID-19 epidemic in Hubei province using the proposed model. Methods: COVID-19 SEIR transmission dynamics model was established, which took transmission ability in latent period and tracking quarantine interventions into consideration. Based on the epidemic data of Hubei province from January 23, 2020 to February 24, 2020, the parameters of the newly established modified SEIR model were fitted. By using Euler integral algorithm to solve the modified SEIR dynamics model, the epidemic situation in Hubei province was analyzed, and the impact of prevention and control measures such as quarantine and centralized treatment on the epidemic development was discussed. Results: The theoretical estimation of the epidemic situation by the modified SEIR epidemic dynamics model is in good agreement with the actual situation in Hubei province. Theoretical analysis showed that prevention and control quarantine and medical follow-up quarantine played an important inhibitory effect on the outbreak of the epidemic.The centralized treatment played a key role in the rapid decline in the number of infected people. In addition, it is suggested that individuals should improve their prevention awareness and take strict self-protection measures to curb the increase in infected people. Conclusion: The modified SEIR model is reliable in the evaluation of COVID-19 epidemic in Hubei province, which provides a theoretical reference for the decision-making of epidemic interventions.

Key words： Coronavirus disease 2019      Severe acute respiratory syndrome coronavirus 2      Novel coronavirus pneumonia      SEIR model      Transmission dynamics      Forecasting     
Received: 20 February 2020      Published: 28 February 2020
CLC:  R181.2+5  
Corresponding Authors: SHI Pengpeng     E-mail: csl1993@stu.xjtu.edu.cn;fphd2017@xjtu.edu.cn;shipengpeng@xjtu.edu.cn
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
CAO Shengli
FENG Peihua
SHI Pengpeng
Cite this article:

CAO Shengli,FENG Peihua,SHI Pengpeng. Study on the epidemic development of COVID-19 in Hubei province by a modified SEIR model. J Zhejiang Univ (Med Sci), 2020, 49(2): 178-184.

URL:

http://www.zjujournals.com/med/10.3785/j.issn.1008-9292.2020.02.05     OR     http://www.zjujournals.com/med/Y2020/V49/I2/178


修正SEIR传染病动力学模型应用于湖北省2019冠状病毒病(COVID-19)疫情预测和评估

目的: 建立可用于2019冠状病毒病（COVID-19）疫情评估的SEIR传染病动力学模型，并对湖北省COVID-19疫情进行预测和评估。方法: 考虑COVID-19潜伏期患者不易被有效隔离，且具有较强的传染能力，建立了联合考虑潜伏期传播能力和追踪隔离干预措施的COVID-19 SEIR传染病动力学模型。以2020年1月23日至2月24日的湖北省疫情数据为依据，拟合得到了新建立的修正SEIR模型的动力学参数。通过欧拉数值方法实现修正SEIR传染病动力学模型的求解，对湖北省疫情进行分析，评估防控隔离和集中收治等措施对疫情发展的影响。结果: 修正的SEIR传染病动力学模型对疫情的理论估计与湖北省疫情的实际情况较为符合。模型理论分析表明，防控隔离和医学追踪隔离等措施对疫情大面积传播有重要抑制作用；集中接收、分层治疗等重要措施对感染人数峰值的迅速回落起到了关键作用；此外，个人提高防范意识，采取严格自我防护措施，遏制了感染人数的新增。结论: 修正的SEIR传染病动力学模型可用于COVID-19传播态势分析，以便为制订未来的疫情干预决策提供一定的理论支持。


关键词： 2019冠状病毒病,  严重急性呼吸综合征冠状病毒2,  新型冠状病毒肺炎,  SEIR模型,  传播动力学,  预测 
Fig 1 Modified SEIR dynamic model
参 数 c δI δq γI
  c：接触率；δI：感染者的隔离速率；δq：隔离接触者向隔离感染者的转化速率；γI：感染者的恢复速率；γH：隔离感染者的恢复速率；β：传染概率；q：隔离比例；α：病死率.
本文取值 2 0.13 0.13 0.007
文献[6]取值 1.6~4.8 0.132 66 0.125 9 0.330 29
取值说明 保持一致 保持一致 保持一致 基于实际治愈人数调整
参 数 γH β q α
本文取值 0.014 2.05×10-9 1×10-6 2.7×10-4
文献[6]取值 0.116 24 2.101 1×10-8 1.888 7×10-7 1.782 6×10-5
取值说明 基于实际治愈人数调整 文献[6]未考虑潜伏期患者传染能力，高估了接触传染概率 参考文献[6]并基于实际数据进行拟合优化 基于实际死亡人数调整
Tab 1 Parameters in modified SEIR model
变 量 S E I Sq Eq H R
  S：易感者；E：接触者；I：感染者；Sq：隔离易感者；Eq：隔离接触者；H：住院患者；R：康复人群.
取值 5917万 4007 524×1.5 2776 400(估) I+Eq 31
取值说明 湖北省总人口官方数据 2020年1月29日确诊人数与1月23日确诊人数的差值 官方数据基础上考虑了未检出比例 官方数据，尚接受医学观察 小于尚在接受医学观察人数 患者隔离与部分医学观察 官方数据
Tab 2 Initial values of the modified SEIR dynamic model
Fig 2 Comparison of the theoretical estimates of the number of the infected and the recovered by the modified SEIR model with and without latent infectivity
Fig 3 Prediction of the trend of COVID-19 epidemic in Hubei province by modified SEIR model
Fig 4 Forecast of COVID-19 epidemic trend in Hubei province after the SEIR model was revised again according to the modification of clinical diagnosis standard
Fig 5 Evaluating the impact of prevention and control measures on epidemic control via the modified SEIR model
Fig 6 Evaluating the impact of medical follow-up quarantineon epidemic control via the modified SEIR model
Fig 7 Evaluating the impact of centralized treatment measures on epidemic control via the modified SEIR model
Fig 8 Evaluating the impact of daily safety protection on epidemic control via the modified SEIR model
[1]   JONATHAN M R, JESSICA RE B, DEREK AT C, et al. Novel coronavirus 2019-nCoV: early estimation of epidemiological parameters and epidemic predictions[J]. MedRxiv, 2020. DOI: 10.1101/2020.01.23.20018549.
[2]   SHEN M W, PENG Z H, XIAO Y N, et al. Modelling the epidemic trend of the 2019 novel coronavirus outbreak in China[J]. bioRxiv, 2020. DOI: 10.1101/2020.01.23.916726.
[3]   WU J T, LEUNG K, LEUNG G M. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study[J]. Lancet, 2020. DOI: 10.1016/S0140-6736(20)30260-9.
[4]   TANG B , WANG X , LI Q et al. Estimation of the transmission risk of 2019-nCov and its implication for public health interventions[J]. J Clin Med, 2020, 9 (2): 462
doi: 10.3390/jcm9020462
[5]   花长春, 陈礼清, 田玉铎.利用SEIR模型推演湖北、非湖北和全国疫情拐点——2020年突发风险系列[EB/OL].(2020-02-07)[2020-02-25].http://finance.sina.com.cn/wm/2020-02-07/doc-iimxyqvz0930302.shtml.
HUA Changchun, CHEN Liqing, TIAN Yuduo. Using SEIR model to deduceepidemic turning points of Hubei, non Hubei and the whole country-Outbreak risk in 2020[EB/OL]. (2020-02-07)[2020-02-25]. http://finance.sina.com.cn/wm/2020-02-07/doc-iimxyqvz0930302.shtml. (in Chinese)
[6]   王霞, 唐三一, 陈勇, 等.新型冠状病毒肺炎疫情下武汉及周边地区何时复工?数据驱动的网络模型分析[J].中国科学: 数学, 2020. DOI: 10.1360/SSM-2020-0037.
WANG Xia, TANG Sanyi, CHEN Yong, et al. When will be the resumption of work in Wuhan and its surrounding areas during COVID-19 epidemic? A data-driven network modeling analysis[J]. Scientia Sinica Mathematica, 2020. DOI: 10.1360/SSM-2020-0037.(inChinese)
[1] HE Yeyan, ZHENG Chanying. Replication and transmission mechanisms of highly pathogenic human coronavirus[J]. J Zhejiang Univ (Med Sci), 2020, 49(3): 324-339.
[2] LUN Yongzhi, LIU Ben, DONG Wen, SUN Jie, PAN Linghong. Comparative analysis of structural characteristics and epitopes in S proteins between SARS-CoV-2 and SARS-CoV[J]. J Zhejiang Univ (Med Sci), 2020, 49(3): 315-323.
[3] XU Yiming, LYU Dandan, YING Kejing. Coagulation dysfunction in COVID-19[J]. J Zhejiang Univ (Med Sci), 2020, 49(3): 340-346.
[4] HU Yan, LI Xiaofeng, GONG Weiyue. Nutritional support for critically ill patients with COVID-19[J]. J Zhejiang Univ (Med Sci), 2020, 49(3): 347-355.
[5] WANG Xiaobo, ZHANG Zhaohui, WU Zhangqiang, SUN Yuezong, ZHANG Yili, GONG Ming, JI Feng. Prediction model of mid-term fatality risk after radical resection in patients with hepatocellular carcinoma based on ALBI-grade[J]. J Zhejiang Univ (Med Sci), 2020, 49(3): 375-382.
[6] WANG Jincheng,LIU Jinpeng,WANG Yuanyuan,LIU Wei,CHEN Xiaoqun,SUN Chao,SHEN Xiaoyong,WANG Qidong,WU Yaping,LIANG Wenjie,RUAN Lingxiang. Dynamic changes of chest CT imaging in patients with COVID-19[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 191-197.
[7] ZHANG Xiaoyan, SUN Wei, SHANG Shiqiang, MAO Jianhua, FU Junfen, SHU Qiang, JIANG Kewen. Principles and suggestions on biosafety protection of biological specimen preservation during prevalence of COVID-19[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 170-177.
[8] CHEN Jun,LIU Danping,LIU Li,LIU Ping,XU Qingnian,XIA Lu,LING Yun,HUANG Dan,SONG Shuli,ZHANG Dandan,QIAN Zhiping,LI Tao,SHEN Yinzhong,LU Hongzhou. A pilot study of hydroxychloroquine in treatment of patients with moderate COVID-19[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 215-219.
[9] CHEN Zhimin,FU Junfen,SHU Qiang,WANG Wei,CHEN Yinghu,HUA Chunzhen,LI Fubang,LIN Ru,TANG Lanfang,WANG Tianlin,WANG Yingshuo,XU Weize,YANG Zihao,YE Sheng,YUAN Tianming,ZHANG Chenmei,ZHANG Yuanyuan. Diagnosis and treatment recommendation for pediatric COVID-19 (the second edition)[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 139-146.
[10] XU Kaijin,CAI Hongliu,SHEN Yihong,NI Qin,CHEN Yu,HU Shaohua,LI Jianping,WANG Huafen,YU Liang,HUANG He,QIU Yunqing,WEI Guoqing,FANG Qiang,ZHOU Jianying,SHENG Jifang,LIANG Tingbo,LI Lanjuan. Management of COVID-19: the Zhejiang experience[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 147-157.
[11] JIANG Saiping,LI Lu,RU Renping,ZHANG Chunhong,RAO Yuefeng,LIN Bin,WANG Rongrong,CHEN Na,WANG Xiaojuan,CAI Hongliu,SHENG Jifang,ZHOU Jianying,LU Xiaoyang,QIU Yunqing. Pharmaceutical care for severe and critically ill patients with COVID-19[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 158-169.
[12] LI Xin,DAI Tian,WANG Hong,SHI Junnian,YUAN Wei,LI Jing,CHEN Lijun,ZHANG Tianming,ZHANG Shanshan,KONG Yan,YUE Ning,SHI Hui,HE Yuping,HU Huifang,LIU Furong,YANG Caixia. Clinical analysis of suspected COVID-19 patients with anxiety and depression[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 203-208.
[13] LUO Song,YANG Lijuan,WANG Chun,LIU Chuanmiao,LI Dianming. Clinical observation of 6 severe COVID-19 patients treated with plasma exchange or tocilizumab[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 227-231.
[14] HONG Dongsheng,NI Jian,SHAN Wenya,LI Lu,HU Xi,YANG Hongyu,ZHAO Qingwei,ZHANG Xingguo. Establishment of a rapid identification of adverse drug reaction program in R language implementation based on monitoring data[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 253-259.
[15] ZHONG Qi,LI Zhi,SHEN Xiaoyong,XU Kaijin,SHEN Yihong,FANG Qiang,CHEN Feng,LIANG Tingbo. CT imaging features of patients with different clinical types of COVID-19[J]. J Zhejiang Univ (Med Sci), 2020, 49(2): 198-202.