新型冠状病毒肺炎的斑块模型:围堵策略对重庆疫情控制的效果讨论

邹兰, 阮士贵

应用数学学报 ›› 2020, Vol. 43 ›› Issue (2) : 310-323.

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应用数学学报 ›› 2020, Vol. 43 ›› Issue (2) : 310-323. DOI: 10.12387/C2020025
新冠肺炎专辑

新型冠状病毒肺炎的斑块模型:围堵策略对重庆疫情控制的效果讨论

    邹兰1, 阮士贵2
作者信息 +

A Patch Model of COVID-19: the Effects of Containment on Chongqing

    ZOU Lan1, RUAN Shigui2
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文章历史 +

摘要

本文利用一个斑块模型研究新型冠状病毒肺炎的地域扩散及控制,通过分析无病平衡点和计算基本再生数,探讨了控制疾病异地和局部扩散的措施.重庆与湖北相邻,人口流动频繁,疫情前期有不少从湖北输入的病例.我们将两个斑块模型用来刻画新型冠状病毒肺炎由湖北向重庆的扩散,通过数值模拟和敏感分析,阐明将封城与其他围堵策略,包括提高病例发现与隔离效率,提高密切接触者追踪与管理效率,增加人际距离,个人预防措施及环境卫生措施等相结合得以消灭疫情.本文所用数据和信息都是国内外权威部门公布的公开数据和信息或经过脱敏处理的数据和信息.

Abstract

In this paper, we constructed a multi-patch endemic model to characterize the geographic spread of the coronavirus disease (COVID-19). Since Hubei was the epicenter of this COVID-19 outbreak in China and Chongqing is a neighbor municipality sharing direct airway, high-speed railway, highway, and waterway transportation, we applied 2-patch model to describe the spatial spread of COVID-19 between these two provinces and to calibrate the reported infected cases data from these two provinces. By preforming the sensitivity analysis of the basic reproduction number in terms of model parameters, we examined the effects of various control strategies such as closing the border, quarantining the exposed individuals, isolating and treating the infected individuals, and so on. It is found that closing the border alone is not enough to control the outbreak and a comprehensive strategy that combines several measures is required to eliminate this infectious disease.

关键词

新型冠状病毒肺炎 / 斑块模型 / 基本再生数 / 地理扩散 / 封城 / 湖北 / 重庆

Key words

COVID-19 / patch model / basic reproduction number / geographic spread / border closing / Hubei / Chongqing

引用本文

导出引用
邹兰, 阮士贵. 新型冠状病毒肺炎的斑块模型:围堵策略对重庆疫情控制的效果讨论. 应用数学学报, 2020, 43(2): 310-323 https://doi.org/10.12387/C2020025
ZOU Lan, RUAN Shigui. A Patch Model of COVID-19: the Effects of Containment on Chongqing. Acta Mathematicae Applicatae Sinica, 2020, 43(2): 310-323 https://doi.org/10.12387/C2020025

参考文献

[1] 中国疾病预防控制中心新型冠状病毒肺炎应急响应机制流行病学组. 新型冠状病毒肺炎流行病学特征分析. 中华流行病学杂志, 2020, 41(2):145-151(Epidemiology Working Group for NCIP Epidemic Response. The epidemiological characteristics of an outbreak of 2019 novel coronavirus diseases (COVID-19) in China. Chinese Journal of Epidemiology, 2020, 41(2):145-151)
[2] World Health Organization (WHO). Coronavirus disease (COVID-19) outbreak. 2020. https://www.who.int/zh/emergencies/diseases/novel-coronavirus-2019
[3] 中华人民共和国卫生健康委员会. 截止3月18日24时新型冠状病毒肺炎疫情最新情况, 2020.3.19(National Health Commission of the People's Republic of China. March 19:Daily briefing on novel coronavirus cases in China. http://www.nhc.gov.cn/yjb/s7860/202003/e644c2fc18b4448bd7ed4b30f68b91a6.shtml)
[4] World Health Organization (WHO). Novel Coronavirus (COVID-19) Situation Report-102, 2020-05-01. https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200501-covid-19-sitrep.pdf?sfvrsn=742f4a18_4
[5] 武汉市人民政府. 市新型冠状病毒感染的肺炎疫情防控指挥部通告(第1号). (The Government of Wuhan. Announcement (No.1) from Control Center of the Epidemic of Novel Coronavirus Pneumonia of Wuhan. http://www.wuhan.gov.cn/hbgovinfo/zwgk_8265/tzgg/,2020)
[6] 襄阳市人民政府. 襄阳市新型冠状病毒感染的肺炎防控指挥部通告. (The Government of Xiangyang. Announcement from Control Center of the Epidemic of Novel Coronavirus Pneumonia of Xiangyang Pneumonia. http://www.xiangyang.gov.cn/zxzx/jrgz/202001/t20200127_2018110.shtml.2020)
[7] 重庆市卫生健康委员会. 2020年2月26日重庆市新冠肺炎疫情情况. (Health Commission of Chongqing. Novel Coronavirus Situation Report of Chongqing, 2020-2-26. http://http://wsjkw.cq.gov.cn/yqxxyqtb/20200226/256287.html,2020)
[8] Meade M S. Emch M, Medical Geography, 3rd ed. New York:Guilford, 2010
[9] Pyle G F. Applied Medical Geography. Washington, D.C.:V.H. Winston & Sons, 1979
[10] Ruan S, Wang W, Levin S A. The effect of global travel on the spread of SARS. Mathematical Bioscience and Engineering, 2006, 3:205-218
[11] Hägerstrand T. Innovation Diffusion as a Spatial Process. Chicago:University of Chicago Press, 1953
[12] Goodall B. The Penguin Dictionary of Human Geography. London:Penguin, 1987
[13] King L J. Central Place Theory. Beverly Hills, CA:Sage Publications, 1984
[14] Li R, Pei S, Chan B, Song Y, Zhang T, Yang W, Shaman J. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2). Science, 2020, 368:489-493
[15] van den Driessche P, Watmough J. Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 2002, 180:29-48
[16] 中华预防医学会新型冠状病毒肺炎防控专家组. 新型冠状病毒肺炎流行病学特征的最新认识. 中华流行病学杂志, 2020, 41(2):139-144(Special Expert Group for Control of the Epidemic of Novel Coronavirus Pneumonia of the Chinese Preventive Medicine Association. An update on the epidemiological characteristics of novel coronavirus pneumonia (COVID-19). Chinese Journal of Epidemiology, 2020, 41(2):139-144)
[17] 王霞, 唐三一, 陈勇, 冯晓梅, 肖燕妮, 徐宗本. 新型冠状病毒肺炎疫情下武汉及周边地区何时复工? 数据驱动的网络模型分析. 中国科学:数学, 2020, 50:1-10(Wang X, Tang S, Chen Y, Feng X, Xiao Y, Xu Z. When will be the resumption of work in Wuhan and its surrounding areas during COVID-19 epidemic? A data-driven network modeling analysis. SCIENTIA SINICA Mathematica, 2020, 50:1-10)
[18] 重庆市卫生健康委员会. 重庆市2018年卫生健康主要统计数据, 2019(Health Commission of Chongqing. The main health statistical data of Chongqing 2018. http://wsjkw.cq.gov.cn/sjfx,2019)
[19] 湖北省卫生健康委员会. 2020年2月25日湖北省新冠肺炎疫情情况. (Health Commission of Hubei Province. Novel Coronavirus Situation Report of Hubei Province, 2020-2-25. http://wjw.hubei.gov.cn/bmdt/ztzl/fkxxgzbdgrfyyq/xxfb/202002/t20200226_2153585.shtml)
[20] Murray J D. Mathematical Biology I!I:Spatial Models and Biomedical Applications. Berlin:Springer-Verlag, 2003
[21] Fisher R A. The wave of advance of advantageous genes. Annanls of Eugenics, 1937, 7:353-369
[22] Bartlett M S. Deterministic and stochastic models for recurrent epidemics. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume 4:Contributions to Biology and Problems of Health. University of California Press, Berkeley, CA, 1956, 81-109
[23] Ruan S, Wu J. Modeling Spatial Spread of Communicable Diseases Involving Animal Hosts, in "Spatial Ecology", R.S. Cantrell, C. Cosner and S. Ruan (eds.). Boca Raton, FL:Chapman & Hall/CRC 2009, 293-316
[24] Yang F, Li W, Ruan S. Dynamics of a nonlocal dispersal SIS epidemic model with Neumann boundary conditions. Journal of Differential Equations, 2019, 267:2011-2051
[25] Sattenspiel L. The Geographic Spread of Infectious Diseases:Models and Applications. Princeton:Princeton University Press, 2009
[26] Arino J. Diseases in metapopulations, in Modeling and Dynamics of Infectious Diseases. Ser. Contemp. Appl. Math. 11. Z. Ma, Y. Zhou, and J. Wu, eds. Singapore:World Scientific, 2009, 65-123
[27] Wang W. Epidemic models with population dispersal. In:"Mathematics for Life Sciences and Medicine", Y. Takeuchi, Y. Iwasa, and K. Sato, eds. Berlin:Springer, 2007, 67-95
[28] Allen L J S, Bolker B M, Lou Y, Nevai A L. Asymptotic profiles of the steady states for an SIS epidemic patch model. SIAM Journal on Applied Mathematics, 2007, 67:1283-1309
[29] Gao D, Dong C. Fast diffusion inhibits disease outbreaks. Proceedings of the American Mathematical Society, 2020, 148:1709-1722
[30] Chen J, Zou L, Jin Z, Ruan S. Modeling the geographic spread of rabies in China. PLoS Neglected Tropical Diseases, 2015, 9:0003772
[31] Gao D, Ruan S. A multi-patch malaria model with demographic structure. SIAM Journal on Applied Mathematics, 2012, 72:819-841
[32] 陈伟, 王晴, 李媛秋, 俞海亮, 夏愔愔, 张慕丽, 秦颖, 张婷, 彭质斌, 张若尘, 杨孝坤, 殷文武, 安志杰, 吴丹, 尹遵栋, 黎舒, 陈秋兰, 冯录召, 李中杰, 冯子健. 我国新型冠状病毒肺炎疫情早期围堵策略概述. 中华预防医学杂志, 2020, 54:239-244(Chen W, Wang Q, Li Y, Yu H, Xia Y, Zhang M, Qin Y, Zhang T, Peng Z, Zhang R, Yang X, Yin W, An Z, Wu D, Yin Z, Li S, Chen Q, Feng L, Li Z, Feng Z. Early containment strategies and core measures for prevention and control of novel coronavirus pneumonia in China. Chinese Journal of Preventive Medicine, 2020, 54:239-244)

基金

国家自然科学基金(11831012;11771168),美国国家自然科学基金(DMS-1853622)资助项目.
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