新型冠状病毒肺炎（COVID-19）疫情自暴发以来，众多研究者基于公开的疫情数据和经典的SEIR模型研究了疫情的发展趋势、传播风险等，为早期COVID-19疫情预测预警提供了重要的决策依据.本论文首先讨论在突发性传染病疫情发展期间，传染病数学模型是如何助力疫情防控的，能在公共卫生重大突发事件中发挥什么样的重要作用.然后集中介绍如何建立数学模型来刻画COVID-19疫情期间密切跟踪隔离措施的实施以及措施强度的变化，重点讨论有症状感染者和确诊病例驱动的追踪隔离措施在建模上的异同，最后得到确诊病例驱动的COVID-19时滞非自治传染病模型.主要结论揭示了确诊滞后不仅能有效延迟感染者类峰值到来的时间，而且使得其出现多峰，甚至最终感染规模可能增大的现象，但是我国强有力的综合防控策略能够有效减缓确诊滞后带来的不利影响.这为分析复杂疫情数据提供了新的重要的模型参考.
Abstract
Since the outbreak of novel Coronavirus pneumonia (COVID-19), many researchers have investigated the development trend of COVID-19 infection, transmission risk and etc. Based on open epidemic data and classic SEIR model, providing important decision basis for early COVID-19 epidemic prediction and early warning. Firstly, this paper discusses how the mathematical models of infectious diseases can help the prevention and control of epidemic situation, and what kind of important role it can play in the major public health emergencies. Then we focus on the formulation of COVID-19 models with contact tracking and quarantine measures during the COVID-19 epidemic, focusing on the similarities and differences between symptomatic infected individual and confirmed individual-driven contact tracing and quarantine measures in terms of mathematical modelling approach, and finally obtain the confirmed individual-driven COVID-19 non-autonomous model with time delay. The main conclusions reveal that the confirmation delay not only can effectively delay the peak, but also can generate multiple outbreaks for the number of exposed (infected) cases, even induce the relatively large final size, but the stringent mitigation strategies can effectively slow down the adverse impact of the confirmation delay. This finding provides a new and important model reference for the analysis of complex epidemic data.
关键词
新型冠状病毒肺炎 /
数学模型 /
跟踪隔离 /
驱动隔离时滞 /
参数估计
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Key words
COVID-19 /
mathematical model /
contact tracing /
quarantine delay /
parameter estimation
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参考文献
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脚注
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基金
国家自然科学基金（11631012，61772017）资助项目.
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