English

运筹学学报 ›› 2020, Vol. 24 ›› Issue (1): 1-12.doi: 10.15960/j.cnki.issn.1007-6093.2020.01.001

• •    下一篇

感染人数期望值估计及新增确诊人数趋势预测的概率模型

丁志伟1, 刘艳云2, 孔京1, 张洪1, 张一3, 戴彧虹4, 杨周旺1,*   

  1. 1. 中国科学技术大学数学科学学院, 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:2020-03-02 发布日期:2020-03-09
  • 通讯作者: 杨周旺 E-mail:yangzw@ustc.edu.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 probability model for estimating the expected number of the newly infected and predicting the trend of the diagnosed

DING Zhiwei1, LIU Yanyun2, KONG Jing1, ZHANG Hong1, ZHANG Yi3, DAI Yuhong4, YANG Zhouwang1,*   

  1. 1. School of Mathematical Sciences, 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:2020-03-02 Published:2020-03-09

PDF

899

摘要： 新型冠状病毒肺炎自2019年12月初出现在武汉后，2020年1月中下旬开始暴发并迅速在全国肆虐，2020年2月中旬后又在几十个国家和地区蔓延，科学有效地掌握疫情发展对于疫情管控至关重要.感染人数是评估疫情形势的重要指标，可以辅助决策者及时制定疫情管控措施.现利用新增确诊人数和新增感染人数存在互相推算的关系，采用极大似然估计方法求解得到全国（除湖北省）每日新增感染人数期望值的估计值，并引入Bootstrap方法给出相应的置信区间，进一步推算现有感染（未确诊）人数并预测新增确诊人数变化趋势，为返城复工提供数据分析支撑.

关键词: 新型冠状病毒, 感染人数, 极大似然估计, EM算法, Bootstrap

Abstract: After 2019 novel cornavirus disease (COVID-19) appeared in Wuhan in early December 2019, it broke out in mid-to-late January 2020 and quickly spread throughout the country. So far, it has spread in dozens of countries and regions, the scientific and efficient understanding of epidemic development is essential for prevention and control. The number of infected people is a key indicator for assessing the situation of the epidemic, helping decision-makers formulate policies in time. This paper uses the maximum likelihood estimation method to obtain estimators of the number of newly infected people across the country except Hubei province. Moreover, Bootstrap simulation enables us to obtain confidence intervals for the estimators. Based on these solutions of the model, we further calculate the number of existing infected but undiagnosed people and predict the trend of the newly diagnosed for the next few days, providing suggestions on returning to work.

Key words: 2019 novel coronavirus, number of the infected, maximum likelihood estimation, EM algorithm, Bootstrap

中图分类号: