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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2020, Vol. 37 ›› Issue (4): 391-402.doi: 10.3969/j.issn.1005-3085.2020.04.001

• •    下一篇

基于反应扩散方程研究新型冠状病毒肺炎在武汉早期传播特征

郭尊光1,2,3,  李明涛4,  常利利5,6,  张  娟5,6,  梁  娟1,2,3,  邢国荣5,6,  张  伟5,6,  孙桂全3,5,6   

  1. 1- 中北大学大数据学院，太原  030051
    2- 太原工业学院理学系，太原  030008
    3- 中北大学理学院，太原  030051
    4- 太原理工大学数学学院，太原  030024
    5- 山西大学复杂系统研究所，太原  030006
    6- 疾病防控的数学技术与大数据分析山西省重点实验室，太原  030006
  • 收稿日期:2020-04-21 接受日期:2020-06-08 出版日期:2020-08-15 发布日期:2020-10-15
  • 通讯作者: 孙桂全 E-mail: gquansun@126.com
  • 基金资助:
    国家自然科学基金(11671241; 11801398)；山西省自然科学基金(201901D111322)；太原工业学院青年(后备)学科带头人支持计划资助项目(201808)；太原工业学院自然科学基金(2016LZ02).

The Early Transmission Characteristics of Corona Virus Disease 2019 Based on the Reaction Diffusion Equation in Wuhan

GUO Zun-guang1,2,3,  LI Ming-tao4,  CHANG Li-li5,6,  ZHANG Juan5,6,  LIANG Juan1,2,3,  XING Guo-rong5,6,  ZHANG Wei5,6,  SUN Gui-quan3,5,6   

  1. 1- Data Science and Technology, North University of China, Taiyuan 030051
    2- Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
    3- School of Science, North University of China, Taiyuan 030051
    4- College of Mathematics, Taiyuan University of Technology, Taiyuan 030024
    5- Complex Systems Research Center, Shanxi University, Taiyuan 030006
    6- Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention, Shanxi University, Taiyuan 030006
  • Received:2020-04-21 Accepted:2020-06-08 Online:2020-08-15 Published:2020-10-15
  • Contact: G. Sun. E-mail address: gquansun@126.com
  • Supported by:
    The National Natural Science Foundation of China (11671241; 11801398); the Natural Science Foundation of Shanxi Province (201901D111322); the Program for the (Reserved) Discipline Leaders of Taiyuan Institute of Technology (201808); the Natural Science Foundation of Taiyuan Institute of Technology (2016LZ02).

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摘要： 本文基于SEIR空间反应扩散模型，研究了新型冠状病毒肺炎在武汉市早期的传播情况．基于中国疾控中心及武汉市卫健委发表文献中公开的数据，提出反应扩散方程的最小二乘法格式，并使用最小二乘法对传染率进行了参数估计，获得了模型参数的最优估计值．在此基础上，基于模型对2019年12月8日至2020年1月5日之间的染病者、潜伏者进行空间传播模拟，模拟显示疾病会从单点暴发发展到多点染病，而且固定空间位置的染病者数量会随着扩散而增大．进一步对扩散速率和传染率进行了敏感性分析，揭示了累计染病者数量会随着传染率和扩散速率的增大而增大，对传染率的敏感性大于其对扩散速率的敏感性．因此，对于突发传染病，及时切断传染源和有效降低传染率是防控传染病进一步蔓延的有效举措，比如早发现早隔离，居家隔离，增加社交距离和外出戴口罩都可以有效降低染病者数量．

关键词: 新型冠状病毒肺炎, 反应扩散方程, 隔离, 参数估计

Abstract: The paper researches the early transmission characteristics of Corona Virus Disease 2019 in Wuhan based on the SEIR (Susceptible-Exposed-Infectious-Removed) spatial reaction diffusion model. In terms of the open data published by China CDC and Wuhan Health Committee, the least square formula of reaction diffusion equation is proposed, then the parameter estimation of the infection rate is calculated by the least square method and the optimal values of model parameters are obtained. The model simulates the spatial transmission of the infected and potential patients from December 8, 2019 to January 5, 2020 showing that the disease will develop from single point outbreak to multi-point infection. In the meantime, the number of patients in fixed space will increase with the spread. Furthermore, the sensitivity analysis of diffusion rate and infection rate reveals that the cumulative number of the infected will increase with the increase of infection rate and diffusion rate, the sensitivity of infection rate is greater than that of diffusion rate. Therefore, for the emergent infectious diseases, timely source cutting-off of infection and effective reduction of infection rate are good measures to the prevention and control to further spread of infectious diseases. For example, the measures of early discovery, early isolation and home isolation, social distance increasing and masks wearing in the outside can effectively reduce the number of the infected.

Key words: new coronavirus pneumonia, reaction diffusion equation, quarantine, parameter estimation

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