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新型冠状病毒肺炎疫情发生后,如何有效应对、疫情何时出现拐点、何时能被有效控制等,已成为全中国乃至全球共同关注的重大问题。
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从目前病例的观察来看,此次武汉疫情的特点主要是病毒具有潜伏期。截至目前,国家卫健委专家表示病毒的平均潜伏期大约在7天左右,最长14天,且在潜伏期也有传染性。而传统的SIR疾病传播模型,缺少对潜伏期的刻画,因此本文选择包含4种状态(易感状态-潜伏状态-感染状态-移出状态)的SEIR模型[4]来对此次武汉市疫情的动力学过程进行分析。
SEIR模型将研究对象分为S、E、I、R 4种类型:
1) S为易感状态(susceptible),表示潜在的可感染人群,个体在感染之前是处于易感状态的,即该个体有可能被邻居个体感染。对应本次疫情,S并不是指城市人口总数,因为并不是所有人都有接触到感染者的机会,在SEIR模型中只有患病群体直接接触到的人才处于易感状态。
2) E为潜伏状态(exposed),表示已经被感染但没有表现出感染症状来的群体。
3) I为感染状态(infected),表示表现出感染症状的人,该个体还会以一定的概率感染其能接触到的易感个体。
4) R为移出状态(removed),表示脱离系统不再受到传染病影响的人(痊愈、死亡或被有效隔离的人)。
记
$S({{t}})$ 、E(t)、I(t)、R(t)分别为时刻t的易感人群数、潜伏人群数、感染人群数、移出人群数,显然有$S({{t}}) + {{E}}({{t}}) + {{I}}({{t}}) + {{R}}({{t}}) \equiv {{N}}$ ,其中N为种群的个体数。假设一个易感状态在单位时间
$\tau $ 里与感染个体接触并被传染的概率为$\beta $ 。由于易感个体的比例为S/N,时刻t网络中总共有I(t)个感染个体,所以易感个体的数目按照如下变化率减小:$$\frac{{{\rm{d}}S}}{{{\rm{d}} t}} = -\frac{{\beta {S\!I}}}{N}$$ 相应地,潜伏个体的数目按照如下变化率增加,并且整体以单位时间概率
${\gamma _1}$ 转化为感染个体:$$\frac{{{\rm{d}} E}}{{{\rm{d}} t}} = \frac{{\beta S\!I}}{N} - {\gamma _1}E$$ 感染个体数目由潜伏群体提供,个体同时以单位时间概率
${\gamma _2}$ 转化为移除状态:$$\frac{{{\rm{d}} I}}{{{\rm{d}} t}} = {\gamma _1}E - {\gamma _2}I$$ 相应地移除个体以概率
${\gamma _2}$ 由感染群体往移除个体转化:$$\frac{{{\rm{d}} R}}{{{\rm{d}} t}} = {\gamma _2}I$$
SEIR-Based COVID-19 Transmission Model and Inflection Point Prediction Analysis
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摘要: 新型冠状病毒肺炎疫情对全国造成了严重影响,社会经济生活受到了极大干扰。该文基于复杂网络理论建立了带有潜伏期的COVID-19流行病SEIR动力学模型,通过设定了3种不同病毒潜伏期情景,依据国家及部分地区疫情数据,针对不同情景对模型参数进行仿真分析,对3种情形下的疫情拐点进行了预测。结果表明,模型分析与疫情发展的真实表现基本吻合。最后提出了加强疫情防控的对策建议,对精准做好疫情防控具有较好的指导作用。Abstract: The COVID-19 has severely affected the country, and people's social and economic lives have been greatly disrupted. Based on the complex network theory, a SEIR dynamic model of the COVID-19 epidemic with a latency period is established in this paper. By setting three scenarios of different incubation periods of the virus, based on national and partial epidemic data, the model parameters are simulated and analyzed for different scenarios. The inflection points of the three cases are predicted, and the results showed that the model analysis is basically consistent with the true performance of the epidemic development. Finally, the paper concludes with specific countermeasures and suggestions for strengthening the prevention and control of the epidemic.
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Key words:
- COVID-19 /
- complex network /
- propagation model /
- SEIR
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