局部新冠肺炎时滞模型及再生数的计算  

A time delay dynamic model with external source and the estimation of reproductive number for the outbreak of novel coronavirus pneumonia

作　　者：刘可伋 江渝 严阅 陈文斌[2] LIU Ke-ji;JIANG Yu;YAN Yue;CHEN Wen-bin(School of Mathematics,Shanghai University of Finance and Economics,Shanghai 200433,China;School of Mathematical Sciences,Fudan University,Shanghai 200433,China;Shanghai Key Laboratory of Financial Information Technology,Shanghai University of Finance and Economics,Shanghai 200433,China)

机构地区：[1]上海财经大学数学学院,上海200433 [2]复旦大学数学科学学院,上海200433 [3]上海财经大学上海市金融信息技术研究重点实验室,上海200433

出　　处：《控制理论与应用》2020年第3期453-460,共8页Control Theory & Applications

基　　金：国家自然科学基金项目(11671098,91630309,11971121);上海科学技术委员会“上海青年科技启明星计划”(19QA1403400)资助.

摘　　要：2019年末的新型冠状病毒肺炎(简称:新冠肺炎,又称COVID–19, novel coronavirus pneumonia, NCP, 2019–nCoV)疫情得到了全球的广泛关注.文献[1–2]提出了一类新的时滞动力学系统的新冠肺炎传播模型(a time delay dynamic model for NCP,简称TDD–NCP模型)来描述疫情的传播过程.本文将这个模型用于研究部分省市的疫情传播问题,通过增加模型的源项用于模拟外来潜伏感染者对于当地疫情的影响.基于全国各级卫健委每日公布的累计确诊数与治愈数,本文有效地模拟并预测了各地疫情的发展.提出了基于TDD模型的再生数的两种计算方法,并做了估计与分析.发现疫情暴发初期再生数较大,但随着各级政府防控力度的加大而逐渐减小.最后,分析了返程潮对上海疫情发展的影响,并建议上海市政府继续加大防控力度,以防疫情二次暴发.In late 2019, the spread of novel coronavirus pneumonia(NCP, COVID–19, or 2019–nCoV) has attracted much attention around the world. In [1–2], a time delay dynamic model(TDD–NCP) was proposed to simulate the outbreak of NCP. In this paper, we add the external source in TDD–NCP to describe the influence of exterior suspected people, and the local outbreak of NCP for some provinces/cities of China are studied. From the number of cumulative confirmed people and cumulative cured people of the Health Commission, we effectively simulate and predict the outbreak of NCP for many districts of China. Moreover, we propose two approaches to calculate the reproductive number. We find that the reproductive number is relatively large initially, and it would decrease as the measures of government enhanced. Finally,we analyze the influence of external returned people for the outbreak of NCP in Shanghai, and we suggest that the local government should apply some more strict measures, otherwise the local cumulative confirmed people of NCP might be out of control.

关 键 词：时滞 输入源项 数学模型 再生数 新型冠状病毒肺炎疫情预测 

分 类 号：O175[理学—数学] R563.1[理学—基础数学]