参赛队号：
#33171
1
第十三届“认证杯”数学中国
数学建模网络挑战赛
承 诺 书
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我们的参赛队号为：33171
我们选择的题目为：C
参赛队员
(
姓名
)
：
队员 1：
柏俊汝
队员
2
：
武海涛
队员 3：
盛华雄
参赛队教练员 (姓名)： 无
参赛队伍组别：研究生组
参赛队号：
#33171
2
第十三届“认证杯”数学中国
数学建模网络挑战赛
编 号 专 用 页
参赛队伍的参赛队号：（请各个参赛队提前填写好）：
33171
竞赛统一编号（由竞赛组委会送至评委团前编号）：
竞赛评阅编号（由竞赛评委团评阅前进行编号）：
参赛队号：
#33171
3
2020 年第十三届“认证杯”数学中国
数学建模网络挑战赛第二阶段论文
关于全球新冠肺炎环境下
题 目
如何安全有效开展复工复产计划以及大型活动的研究
摘 要：
随着全球新冠疫情拐点的到来，如何有效安全地开展复工、复产计划成为各国重点
关注的问题。本文通过建立 SEIAR 模型，从整体上研究评估了各个国家出现第二次高峰
的风险，确定了未来疫情发展趋势以及疫情防控措施将受哪些因素的主要影响，并引入
戴口罩的 Wells-Riley 疾病感染概率预测模型给出了大型体育赛事的重启时间表。
针对问题
1
，我们结合现阶段疫情发展情况，建立了 SEIAR 模型，通过加入无症状
感染者 A，以及政府力度和民众警惕程度等影响因素，分别对中国、法国、伊朗三个国
家的疫情发展情况进行了研究，结果表明在各国现有防疫政策措施下，中国不太可能出
现第二次高峰，法国和伊朗则有较大可能出现第二次高峰。并针对中国如何避免第二次
高峰提出了建议。
针对问题
2
，首先根据当前对疾病的掌握情况确定不易测量的疾病特征，主要包括
潜伏期的长度分布、无症状感染者的比例、通常的测试方法对潜伏期和无症状感染者的
假阴性率和假阳性率等。其次引入这些特征作为变量参数对 SEIAR 模型进行修正，并确
定模型中影响防疫干预强度的变量参数。通过对疾病特征参数对疾病流行的影响分析可
以发现，在有效控制疫情的情况下这些不易测量的疾病特征不会使疫情发生逆转。需要
注意的是潜伏期长度与检测假阴性率这两个参数会影响无症状感染者与潜伏者的数量
变化，在这两类人群传染能力相比于确诊者较低时不会影响疫情发展趋势，但当这两类
人群的传染能力略微提升后，疫情将出现二次高峰。通过对不同干预强度对疾病流行的
影响分析可以得到，目前还尚未到达完全解除疫情的阶段，当防疫干预强度参数超过 5
时便会引起疫情二次高峰，需要警惕。同时，采取逐步降低干预强度的策略，可以在疫
情有效控制之下尽可能快的恢复疫情前的生产生活秩序。
针对问题
3
，将疾病传播有效再生数
R
t
作为衡量疫情防控安全级别的关键系数，在
R
t
<1 的前提下，将安全状况分为 5 个级别。用引入戴口罩的 Wells-Riley 疾病感染概率
预测模型计算各类体育赛事的观众感染新冠肺炎的概率 P 和有效再生数 R
t
。在第一阶段
用
Holt
模型对全国无症状感染者进行预测和残差分析，取得较好效果。在此基础上，收
集热门的 5 类体育赛事观众人数、场馆大小、比赛时长等基本信息进行综合动态分析评
估，得出了各大体育赛事重启的时间表。评估可知，当前各大体育赛事的疾病有效再生
数
R
t
大于
1
，不具备重启比赛的基本条件；
LPL
英雄联盟联赛最早具备开赛条件，预计
5 月底可进行无观众比赛。
针对问题 4，结合问题 3 的模型评估，给国家卫健委写备忘录，对体育赛事重启过
程的疫情控制方法提出建议。
关 键 词
无症状感染者，有效再生系数，SEIAR 模型，Wells-Riley 模型
参赛队号：
#33171
4
Abstract
With the arrival of the inflection point of the global 2019-nCoV, how to effectively and
safely carry out resumption of work and production has become a key issue for all countries.
In this paper, through the establishment of the SEIAR model, the overall assessment of the
risk of the second peak in various countries has been conducted, the future outbreak
development trends and the factors that will be affected by the outbreak prevention and
control measures will be determined, and the Wells-Riley disease with a mask infection
probability prediction model gives the restart schedule of large sports events.
For question 1,we established the SEIAR model in combination with the current
situation of the outbreak. By adding asymptomatic infected A, as well as the government's
strength and public vigilance and other influencing factors, the outbreaks in China, France and
Iran were developed. A study has been conducted and the results show that under the current
national epidemic prevention policy measures, China is unlikely to have a second peak, while
France and Iran are more likely to have a second peak. And put forward suggestions on how
to avoid the second peak in China.
For question 2, Firstly, determine the characteristics of the disease that are not easy to
measure based on the current grasp of the disease, including the incubation period, the
proportion of asymptomatic infections, and the false negative rate and false positive rate of
the usual test methods for the incubation period and asymptomatic infections. Secondly, these
features are introduced as variable parameters to modify the SEIAR model and determine the
variable parameters that affect the intensity of the epidemic prevention intervention in the
model. Through the analysis of the influence of disease characteristic parameters on disease
epidemic, it can be found that these disease characteristics that are not easy to measure under
the condition of effective control of the epidemic will not reverse the epidemic. It should be
noted that the two parameters, the length of the incubation period and the false negative rate
of the test, will affect the change in the number of asymptomatic infected persons and latent
persons. When the infectivity of these two groups of people is lower than that of the
diagnosed, it will not affect the development trend of the epidemic. But when the infectious
ability of these two groups of people is slightly improved, the epidemic will have a second
peak. It can be obtained by analyzing the impact of different intervention intensity on the
epidemic of disease. At present, it has not yet reached the stage of completely eliminating the
epidemic. When the intensity of the epidemic prevention intervention parameter exceeds 5, it
will cause the second peak of the epidemic, which requires vigilance. At the same time,
adopting a strategy of gradually reducing the intensity of intervention can restore the
production and living order before the epidemic as quickly as possible under the effective
control of the epidemic.
For question 3
，
the effective regeneration number R
t
of disease transmission is taken as
the key factor to measure the safety level of epidemic prevention and control. Under the
premise of R
t
< 1, the safety status is divided into five levels. The probability of NCP and the
effective regeneration number R
t
were calculated by using the Wells-Riley Infection
参赛队号：
#33171
5
Prediction Model with a mask to calculate the P of the new crowns pneumonia in all sports
events. In the first stage, Holt model was used to predict and analyze the residuals of
asymptomatic patients in China. On this basis, the basic information such as the number of
spectators, the size of venues and the duration of the five popular sports events are collected
for comprehensive dynamic analysis and evaluation, and the timetable for the restart of major
sports events is obtained. It can be seen from the evaluation that the effective number of
disease regeneration RT of current major sports events is greater than 1, which does not meet
the basic conditions for restarting the competition; LPL League of heroes is the first to meet
the conditions for opening the competition, and it is expected that there will be no spectator
competition at the end of May.
For question 4, a memorandum was written to the national health and Health
Commission to make suggestions on the epidemic control methods in the process of sports
event restart.
Key words： Asymptomatic infection , R , SEIAR, Wells-Riley
