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运筹学学报 ›› 2020, Vol. 24 ›› Issue (3): 27-42.doi: 10.15960/j.cnki.issn.1007-6093.2020.03.002

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动态传播率模型及其在疫情分析中的应用

胡云鹤1, 刘艳云2, 吴凌霄1, 王杰1, 孔京1, 张一3, 戴彧虹4,*, 杨周旺1   

  1. 1. 中国科学技术大学, 合肥 230026;
    2. 北京大学数学科学学院, 北京 100871;
    3. 北京大数据研究院, 北京 100871;
    4. 中国科学院数学与系统科学研究院, 北京 100190
  • 收稿日期:2020-03-16 发布日期:2020-09-05
  • 通讯作者: 戴彧虹 E-mail:dyh@lsec.cc.ac.cn
  • 基金资助:
    国家自然科学基金（Nos.71950011，11871447，71991464/71991460），国家重点研发计划课题（No.2018AAA0101001）

A dynamic transmission rate model and its application in epidemic analysis

HU Yunhe1, LIU Yanyun2, WU Lingxiao1, WANG Jie1, KONG Jing1, ZHANG Yi3, DAI Yuhong4,*, YANG Zhouwang1   

  1. 1. University of Science and Technology of China, Hefei 230026, China;
    2. School of Mathematical Sciences, Peking University, Beijing 100871, China;
    3. Beijing Institute of Big Data Research, Beijing 100871, China;
    4. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2020-03-16 Published:2020-09-05

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摘要： 应用数据驱动的动态传播率来代替基本传染数$R_0$，在全国和省市两个层面上研究COVID-19疫情发展的特点和趋势。首先，基于动态增长率建立传染病常微分方程，推导得出动态传播率模型。其次，选择幂函数作为动态传播率的拟合函数，以3天作为最优滑窗期，对各地拐点进行了估计。最后，通过动态模型对各地不同程度尾声开始的起点进行了预测，并在13个省市间进行9个疫情相关指标的对比分析。结果显示，各地动态传播率在经过短暂的波动后均稳步下降，疫情得到有效控制；估计的拐点主要集中在2月中旬，而预测的尾声都将在3月底之前到来；同时，各地疫情发展特点和趋势、防控措施力度和效果存在一定差异。

关键词: COVID-19, 现存病例数, 动态增长率, 动态传播率, 拐点, 尾声

Abstract: This paper applies a data-driven dynamic transmission rate to replace the basic reproduction number $R_0$ and studies the characteristics and trends of the development of COVID-19 at both national and provincial levels. Firstly, based on the dynamic growth rate, an ordinary differential equation for infectious diseases is established, which can derive the dynamic transmission rate model. Secondly, this paper selects the power function as the fitting function of the dynamic transmission rate, and uses 3 days as the optimal sliding window period to estimate the inflection points in different regions. Finally, using the dynamic model, this paper predicts the starting point of the end phase of the epidemic at different levels in various places, and then compares and analyzes 9 epidemic-related indicators among 13 provinces and cities. The results show that the dynamic transmission rates in all regions have steadily declined after a brief fluctuation, which means the epidemic situation has been effectively controlled; the date of the estimated inflection points are mainly concentrated in mid-February, and the predicted end phase will come before the end of March; at the same time, there are some differences in the characteristics and trends of the epidemic situation as well as the intensity and effectiveness of prevention and control measures.

Key words: COVID-19, existing infected case number, dynamic growth rate, dynamic transmission rate, inflection point, end phase

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