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运筹学学报 ›› 2021, Vol. 25 ›› Issue (1): 17-30.doi: 10.15960/j.cnki.issn.1007-6093.2021.01.002

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非线性组合动态传播率模型与我国COVID-19疫情分析和预测

谢晓金1, 罗康洋1, 张怡1, 金建炳2, 林海翔3, 殷志祥1, 王国强1,*()   

  1. 1. 上海工程技术大学数理与统计学院, 上海 201620
    2. 南京信息工程大学环境科学与工程学院, 南京 210044
    3. 代尔夫特理工大学代尔夫特应用数学研究所, 代尔夫特 2628 XE, 荷兰
  • 收稿日期:2020-07-22 出版日期:2021-03-15 发布日期:2021-03-05
  • 通讯作者: 王国强 E-mail:guoq_wang@hotmail.com
  • 作者简介:王国强 E-mail: guoq_wang@hotmail.com
  • 基金资助:
    国家自然科学基金(11971302);国家自然科学基金(62072296);全国统计科学研究项目(2020LY067)

Nonlinear combinational dynamic transmission rate model and COVID-19 epidemic analysis and prediction in China

Xiaojin XIE1, Kangyang LUO1, Yi ZHANG1, Jianbing JIN2, Haixiang LIN3, Zhixiang YIN1, Guoqiang WANG1,*()   

  1. 1. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China
    2. School of Environmental Science and Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China
    3. Delft Institute of Applied Mathematics, DelftUniversity of Technology, Delft 2628 XE, the Netherlands
  • Received:2020-07-22 Online:2021-03-15 Published:2021-03-05
  • Contact: Guoqiang WANG E-mail:guoq_wang@hotmail.com

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摘要：

针对传统的流行性传染病学中基本传染数$R_0$难以准确估计以及单一模型预测精度低的缺陷，利用组合动态传播率替换基本传染数$R_0$，提出基于支持向量回归的非线性时变传播率模型并对我国COVID-19疫情进行分析和预测。首先，计算动态传播率的离散值；其次，使用多项式函数、指数函数、双曲函数和幂函数分别对动态传播率的离散值进行拟合并基于最佳滑窗期$k=3$构建相应的预测模型；接着，基于拟合优度等评价指标选择最佳的三种单一模型并对其预测结果进行非线性组合；最后，利用非线性组合动态传播率模型对湖北、全国除湖北和全国COVID-19疫情进行分析和预测。实证结果表明提出的非线性组合动态传播率模型对不同地区COVID-19疫情数据的预测误差均相对较小；对重点省市COVID-19疫情的拐点预测切实合理；湖北、全国除湖北与全国自2020年2月27日起后20天疫情预测曲线的拟合优度分别为98.53%、98.06%和97.98%。

关键词: COVID-19, 新冠肺炎疫情, 动态传播率, 组合预测模型, 支持向量回归

Abstract:

Due to the difficulty in accurately estimating the basic infectious number $R_0$ and the low accuracy of single model prediction, the traditional epidemic infectious diseases studying is blocked and not widely implemented operationally. To overcome this challenge, this paper proposes a non-linear model with time varying transmission rate based on the support vector regression instead of basic infection number $R_0$. The non-linear model is applied to analyze and predict the COVID-19 outbreak in China. Firstly, the discrete values of the dynamic transmission rate are calculated. Secondly, the polynomial function, exponential function, hyperbolic function and power function are used to fit with the discrete values of the dynamic transmission rate and the corresponding prediction model is rebuilt on basis of the optimal sliding window period $k=3$. Then, on account of the evaluation indexes such as goodness of fitting, the best three prediction models are selected, and the prediction results are nonlinearly combined. Finally, the combined dynamic transmission rate model is used to analyze and predict the COVID-19 epidemic in Hubei province, outside-Hubei provinces, and the whole China. The empirical results show that the combined dynamic transmission rate model is in relatively good agreement with the COVID-19 epidemic data in different regions. The prediction of COVID-19 epidemic infection points in most provinces well reproduce the real situation. The goodness of fitting of the epidemic prediction curves in Hubei province, outside-Hubei provinces and the whole China from February 27, 2020 are 98.53%, 98.06% and 97.98%, respectively.

Key words: COVID-19, 2019-nCOV, dynamic transmission rate, combined prediction model, support vector regression

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