[1]曹 祯,聂麟飞*.具有迁移效应和隔离措施的COVID-19传播模型分析[J].江西师范大学学报(自然科学版),2021,(06):551-558.[doi:10.16357/j.cnki.issn1000-5862.2021.06.01]
　CAO Zhen,NIE Linfei*.The Analysis of COVID-19 Transmission Model with Migration Effect and Isolation Measure[J].Journal of Jiangxi Normal University:Natural Science Edition,2021,(06):551-558.[doi:10.16357/j.cnki.issn1000-5862.2021.06.01]
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具有迁移效应和隔离措施的COVID-19传播模型分析()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2021年06期
页码:
551-558
栏目:
新型冠状病毒肺炎疫情防控
出版日期:
2021-11-25

文章信息/Info

Title:
The Analysis of COVID-19 Transmission Model with Migration Effect and Isolation Measure
文章编号:
1000-5862(2021)06-0551-08
作者:
曹 祯; 聂麟飞*
新疆大学数学与系统科学学院,新疆 乌鲁木齐 830046
Author(s):
CAO Zhen; NIE Linfei*
College of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830046,China
关键词:
COVID-19传播模型;  人口迁移与自我防护;  基本再生数;  无病平衡点;  稳定性与持久性
Keywords:
COVID-19 transmission model;  population migration and self-protection;  basic reproduction number;  disease-free equilibrium;  stability and persistence
分类号:
O 175; R 181.8
DOI:
10.16357/j.cnki.issn1000-5862.2021.06.01
文献标志码:
A
摘要:
基于COVID-19传播过程中人口流动的必然性、无症状感染者的普遍性和隔离策略的有效性,该文提出了一类具有迁移效应、无症状感染者、自我防护意识和隔离策略的COVID-19传播动力学模型,利用下一代矩阵方法给出了各类子系统和全系统基本再生数的精确表达式.进一步地,通过采用线性近似理论,构造Lyapunov函数、比较原理等方法,得到了无病平衡点的全局渐近稳定性以及疾病的持久性.最后,数值模拟解释了主要的理论结果以及人口的迁移和隔离对疾病传播的影响.
Abstract:
Based on the inevitability of population flow in the process of COVID-19 transmission,the universality of asymptomatic infection and the effectiveness of isolation strategy,the COVID-19 transmission dynamics model with migration effect,asymptomatic infection,self-protection consciousness and isolation strategy is proposed,and the next generation matrix method is used to give the exact expression of the basic production numbers of all kinds of subsystems and the whole system.Furthermore,by using the linear approximation theory,constructing Lyapunov stability theory,comparison principle,etc.,the global asymptotic stability of the disease-free equilibrium and the persistence of this disease are obtained.Finally,numerical simulations are performed to explain the main theoretical results and the impact of population migration and isolation on disease transmission.

参考文献/References:

[1] 胡義,王开发,王稳地.2019新型冠状病毒肺炎疫情传播能力及疫情控制效能的地域差异分析[J].应用数学学报,2020,43(2):227-237.
[2] 黄森忠,彭志行,靳祯.新型冠状病毒肺炎疫情控制策略研究:效率评估及建议[J].中国科学:数学,2020,50(6):885-898.
[3] 翟羿江,蔺小林,李建全,等.基于存在基础病史易感者的SEIR模型对COVID-19传播的研究[J].应用数学和力学,2021,42(4):413-421.
[4] Tang Biao,Wang Xia,Li Qian,et al.Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions[J].Journal of Clinical Medicine,2020,9(2):462.
[5] 白宁,宋晨玮,徐瑞,等.基于动力学模型的COVID-19疫情预测与控制策略研究[J].应用数学学报,2020,43(3):483-493.
[6] 崔景安,吕金隆,郭松柏,等.新发传染病动力学模型:应用于2019新冠肺炎传播分析[J].应用数学学报,2020,43(2):147-155.
[7] 朱宏淼,齐佳音,靳祯,等.重大公共卫生事件中公众防控意识传播模型研究[J].系统工程理论与实践,2021,41(11):2865-2875.
[8] 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[J].应用数学学报,2020,43(2):310-323.
[9] 王霞,唐三一,陈勇,等.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[J].中国科学:数学,2020,50(7):969-978.
[10] Sun Xiaodan,Xiao Yanni,Ji Xiangting.When to lift the lockdown in Hubei province during COVID-19 epidemic?An insight from a patch model and multiple source data[J].Journal of Theoretical Biology,2020,507:110469.
[11] 朱翌民,黄勃,王忠震,等.隔离措施对COVID-19疫情控制的模型分析[J].武汉大学学报:理学版,2020,66(5):442-450.
[12] 李倩,肖燕妮,吴建宏,等.COVID-19疫情时滞模型构建与确诊病例驱动的追踪隔离措施分析[J].应用数学学报,2020,43(2):238-250.
[13] 王雪萍,王晓静,白玉珍,等.一类潜伏期和隐性感染者均具有传染性的COVID-19传染病模型[J].应用数学进展,2020,9(5):700-707.
[14] 张菊平,李云,姚美萍,等.武汉市COVID-19疫情与易感人群软隔离强度关系分析[J].应用数学学报,2020,43(2):162-173.
[15] Martcheva M,Antman S,Holmes P.An introduction to mathematical epidemiology[M].3rd ed.New York:Springer,2015.
[16] Sun Chengjun,Yang Wei,Arino J,et al.Effect of media-induced social distancing on disease transmission in two patches setting[J].Mathematical Biosciences,2011,230(2):87-95.
[17] Thieme H R.Persistence under relaxed point-dissipativity:with application to an endemic model[J].SIAM Journal on Applied Mathematics,1993,24(2):407-435.

备注/Memo

备注/Memo:
收稿日期:2021-05-14
基金项目:国家自然科学基金(11961066)和新疆维吾尔自治区自然科学基金(2021D01E12,2021D01C070)资助项目.
通信作者:聂麟飞(1978—),男,河南扶沟人,教授,博士,主要从事微分方程理论及其应用研究.E-mail:lfnie@163.com
更新日期/Last Update: 2021-11-25