COVID-19在公交网络传播模型及防疫策略有效性分析

牟振华; 李想; 闫康礼; 郭继杰

doi:10.3963/j.jssn.1674-4861.2021.01.0013

COVID-19在公交网络传播模型及防疫策略有效性分析

doi: 10.3963/j.jssn.1674-4861.2021.01.0013

1.
山东建筑大学交通工程学院济南 250101
2.
济南轨道交通集团有限公司济南 250101

基金项目:

教育部人文社科基金项目 19YJC630124

详细信息

通讯作者:
牟振华（1983—），博士，副教授.研究方向：交通运输规划与管理.E-mail: mouzhenhua@sdjzu.edu.cn

中图分类号: U495
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出版历程
- 收稿日期: 2020-09-05
- 刊出日期: 2021-02-28

An Analysis of COVID-19 Propagation Model in Public Transportation Networks and Effectiveness of Epidemic Prevention Strategies

1.
School of Transportation Engineering, Shandong Jianzhu University, Jinan 250101, Shandong, China
2.
Jinan Rail Transit Group Co., Ltd, Jinan 250101, Shandong, China

摘要

摘要: 城市公交系统是空气传播型病毒进行人际传播的重要潜在空间，研究病毒在公交系统中的传播，能精确的指导公交防疫策略的制定。基于双层公交网络模型，耦合出行规则和SEIR模型建立了公交网络传播模型，以某虚拟的区域空间和公交线网为背景，根据双层网络模型的特点，分析了公交车上及公交站点病毒传播的过程，制定宏观和微观2种防疫策略并分析效果。研究发现，公交出行会导致病毒大范围传播，公交车上和公交站点是最重要的传播环节。对公交防疫策略效果的分析中，宏观控制策略的切断公交线路比例φ₁ >0.5或者停运公交站点比例 φ₂ >0.4时，最终免疫人群比例会下降至0.3以下。微观调节策略则需要同时调整发车间隔 t_d < 4且满载率α < 50%，则最终免疫人群比例小于0.4，防控效果最显著。
- 交通仿真 /
- 公交线网 /
- 病毒传播 /
- 防控策略 /
- 复杂网络 /
- SEIR模型
Abstract: Public transportation system is a critical potentiality space where airborne viruses have to spread between people. The study of the spread of viruses in the public transport system can accurately guide public transport epidemic prevention strategies. The two-layer public transportation network model, particle travel rules, and SEIR model are used to establish a public transportation network propagation model. Based on the background of virtual regional space and bus line network, characteristics of the two-layer network model are used to analyze the process of virus transmission on the bus and at the bus station. Both macro and micro epidemic prevention strategies are developed to analyze their effects. Public transportation causes the virus to spread on a large scale, and buses and bus stops are the most critical transmission links. For the public transportation epidemic prevention strategy, when the macro-control strategy cuts off the proportion of public transportation lines φ₁ >0.5 or stops the proportion of public transportation stations φ₂ >0.4, the final proportion of the immunized population will drop to below 0.3. The micro-adjustment strategy needs to control the departure interval t_d < 4 and the full load rate simultaneously α < 50%, so the final immune population ratio is less than 0.4, with the optimal prevention and control effect.
- traffic simulation /
- public transportation networks /
- virus transmission /
- prevention and control strategy /
- complex network /
- SEIR model

HTML全文

图 1 公交网络模型示意图

Figure 1. Bus network model

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图 2 粒子出行示意图

Figure 2. Particle travel

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图 3 有无公交情况下的感染结果

Figure 3. Infection results with/without public transportation

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图 4 不同出行概率的感染结果

Figure 4. Infection results with different travel probabilities

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图 5 公交节点感染人数占比

Figure 5. Proportion of infected people in bus nodes

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图 6 不同 p_c值的感染人群比例曲线

Figure 6. Proportion curve of the infected population with different values p_c

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图 7 不同发车间隔下的感染结果

Figure 7. Infection results at different departure intervals

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图 8 不同满载率下的感染结果

Figure 8. Infection results at different full load rates

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图 9 不同度公交站点上的累计感染人数

Figure 9. Number of infections in bus nodes of different degrees

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图 10 宏观控制策略效果

Figure 10. Macro-containment strategy effect

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图 11 最终免疫人群比例与满载率和发车间隔关系

Figure 11. Relationship among the proportion of final immune population, the full load rate, and the departure interval

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参考文献(20)

[1]	ZHANG Jinnong, ZHOU Luqian, YANG Yuqiong, et al. Therapeutic and triage strategies for 2019 novel coronavirus disease in fever clinics[J]. The Lancet Respiratory Medicine, 2020, 8 (3): 11-12. doi: 10.1016/S2213-2600(20)30071-0
[2]	XU Zhe, SHI Lei, WANG Yijin, et al. Pathological findings of COVID-19 associated with acute respiratory distress syndrome[J]. The Lancet RespiratoryMedicine, 2020, 8(4): 420-422. doi: 10.1016/S2213-2600(20)30076-X
[3]	中国疾病预防控制中心. 新型冠状病毒肺炎流行病学特征分析[J]. 中华流行病学杂志, 2020, 41(2): 145-151. doi: 10.3760/cma.j.issn.0254-6450.2020.02.003 Chinese Center for Disease Control and Prevention. The epidemiological characteristics of an outbreak of 2019 novel coronavirus diseases(COVID-19)in China[J]. Chinese Journal of Epidemiology, 2020, 41(2): 145-151. (in Chinese) doi: 10.3760/cma.j.issn.0254-6450.2020.02.003
[4]	种鹏云, 尹惠. 交通运输传播新型冠状病毒肺炎的系统动力学仿真[J]. 交通运输工程学报, 2020, 20(3): 100-109. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003013.htm ZHONG Pengyun, YIN Hui. System dynamics simulation on spread of COVID-19 by traffic and transportation[J]. Journal of Traffic and Transportation Engineering, 2020, 20(3): 100-109. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003013.htm
[5]	雷斌, 刘星良, 曹振, 等. COVID-19在城市轨道交通系统内的传播建模与预测[J]. 交通运输工程学报, 2020, 20(3): 139-149. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003017.htm LEI Bin, LIU Xingliang, CAO Zhen et al. Modeling and forecasting of COVID-19 spread in urban rail transit system[J]. Journal of Traffic and Transportation Engineering, 2020, 20 (3): 139-149. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003017.htm
[6]	马昌喜, 王超, 郝威, 等. 突发公共卫生事件下应急定制公交线路优化[J]. 交通运输工程学报, 2020, 20(3): 89-99. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003012.htm MA Changxi, WANG Chao, HAO Wei, et al. Emergency customized bus route optimization under public health emergencies[J]. Journal of Traffic and Transportation Engineering, 2020, 20(03): 89-99. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003012.htm
[7]	鲍君忠, 秦莹, 王西召, 等. 基于Logistic模型的大型邮轮疫情预测分析[J]. 交通信息与安全, 2020, 38(2): 136-142+148. https://www.cnki.com.cn/Article/CJFDTOTAL-JTJS202002020.htm BAO Junzhong, QIN Ying, WANG Xizhao, et al. A prediction and analysis of epidemic outbreaks on large cruise ships based on a logistic model[J]. Journal of Transport Information and Safety, 2020, 38(2): 136-142+148. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JTJS202002020.htm
[8]	刘文君, 何新华, 胡文发. 重大突发疫情对港口运营能力的影响研究[J]. 交通信息与安全, 2020, 38(2): 102-111+119. https://www.cnki.com.cn/Article/CJFDTOTAL-JTJS202002016.htm LIU Wenjun, HE Xinhua, HU Wenfa. Impacts of major epidemic in public health emergencies on operational capacity of ports[J]. Journal of Transport Information and Safety. 2020, 38 (2): 102-111+119. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JTJS202002016.htm
[9]	周继彪, 马昌喜, 董升, 张敏捷. 新冠肺炎疫情下城市公共交通非常规防疫策略: 以宁波市为例[J]. 中国公路学报, 2020, 33(11): 1-10. ZHOU Jibiao, MA Changxi, DONG Sheng, et al. Unconventional prevention strategies for urban public transport in the COVID-19 epidemic: taking ningbo city as a case study[J]. China Journal of Highway and Transport, 2020, 33(11): 1-10. (in Chinese)
[10]	RUAN Zhongyuan, TANG Ming, LIU Zonghua. How the contagion at links influences epidemic spreading[J]. The European Physical Journal B, 2013(86): 149. doi: 10.1140/epjb/e2013-30914-9
[11]	SONG Chaoming, QU Zehui, BLUMM N, et al. Limits of predictability in human mobility[J]. Science, 2010(327): 1018-1021. http://bjsm.bmj.com/lookup/ijlink?linkType=ABST&journalCode=sci&resid=327/5968/1018&atom=%2Fbjsports%2F45%2F16%2F1272.atom
[12]	TANG Ming, LIU Zong, LI Baowen. Epidemic spreading by objective traveling[J]. Europhys Lett, 2009(87): 18005.
[13]	阮中远. 复杂网络上的流行病传播[J]. 中国科学: 物理学、力学、天文学, 2020, 50(1): 98-117. https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK202001008.htm RUAN Zhongyuan. Epidemic spreading in complex networks[J]. Scientia Sinica(Physica, Mechanica & Astronomica), 2020, 50(1): 98-117. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK202001008.htm
[14]	茹小磊, 杨超, 严钢, 等. 应对突发大规模流行病的城市常规公交管控策略[J]. 中国公路学报, 2020, 33(11): 11-19. doi: 10.3969/j.issn.1001-7372.2020.11.003 RU Xiaolei, YANG Chao, YAN Gang, et al. Control strategy of urban public transit in response to large-scale emergent epidemic[J]. China Journal of Highway and Transport. 2020, 33 (11): 11-19. (in Chinese) doi: 10.3969/j.issn.1001-7372.2020.11.003
[15]	COLIZZA V, PASTOR-SATORRAS R, VESPIGNANI A. Reaction-diffusion processes and metapopulation models in heterogeneous networks[J]. Nat Phys, 2007(3): 276-282. http://www.nature.com/articles/nphys560?error=cookies_not_supported&code=02f2cdd7-a776-42b1-8821-a8925e9329aa
[16]	范如国, 王奕博, 罗明, 等. 基于SEIR的新冠肺炎传播模型及拐点预测分析[J]. 电子科技大学学报, 2020, 49(3): 369-374. https://www.cnki.com.cn/Article/CJFDTOTAL-DKDX202003009.htm FAN Ruguo, WANG Yibo, LUO Ming, et al. SEIR-Based COVID-19 transmission model and inflection point prediction analysis[J]. Journal of University of Electronic Science and Technology of China, 2020, 49(3): 369-374. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DKDX202003009.htm
[17]	张宇, 田万利, 吴忠广, 等. 基于改进SEIR模型的新冠肺炎疫情沿交通线路传播机制[J]. 交通运输工程学报, 2020, 20 (3): 150-158. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003018.htm ZHANG Yu, TIAN Wanli, WU Zhongguang, et al. Transmission mechanism of COVID-19 epidemic along traffic routes based on improved SEIR model[J]. Journal of Traffic and Transportation Engineering, 2020, 20(3): 150-158. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202003018.htm
[18]	SMALL M, TSK C K. Small world and scale free model of transmission of SARS[J]. Intertional Journal of Bifurcation and Chaos, 2005, 15(5): 1745-1755. doi: 10.1142/S0218127405012776
[19]	倪顺江. 基于复杂网络理论的病毒动力学建模与研究[D]. 北京: 清华大学, 2009. NI Shunjiang. Research on modeling of infectious disease spreading based on complex network theory[D]. Beijing: Tsinghua University, 2009. (in Chinese)
[20]	缪超. 具有多感染率网络中的传播动力学及节点免疫策略[D]. 南京: 南京邮电大学, 2018. MIU Chao. Epidemic dynamics and node immunization strategy in a network with multiple infection rates[D]. Nanjing: Nanjing University of Posts and Telecommunications, 2018. (in Chinese)