基于人口流动的COVID-19传播动力学模型研究

郭文丹; 聂麟飞

doi:10.13568/j.cnki.651094.651316.2021.03.18.0002

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基于人口流动的COVID-19传播动力学模型研究

数理科学 | 更新时间：2026-01-21

- 基于人口流动的COVID-19传播动力学模型研究
- 基于人口流动的COVID-19传播动力学模型研究
- 新疆大学学报（自然科学版中英文） 2022年39卷第2期页码：161-168
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
  
  国家自然科学基金项目(11961066);新疆维吾尔自治区高校科研计划项目(XJEDU2018I001)
- DOI：10.13568/j.cnki.651094.651316.2021.03.18.0002
  中图分类号： R563.1;O175
- 纸质出版：2022
- 稿件说明：
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[1]郭文丹,聂麟飞.基于人口流动的COVID-19传播动力学模型研究[J].新疆大学学报(自然科学版)(中英文),2022,39(02):161-168.
[1]郭文丹,聂麟飞.基于人口流动的COVID-19传播动力学模型研究[J].新疆大学学报(自然科学版)(中英文),2022,39(02):161-168. DOI： 10.13568/j.cnki.651094.651316.2021.03.18.0002.

DOI：10.13568/j.cnki.651094.651316.2021.03.18.0002.

摘要

地区之间的人口流动是当前乃至今后一段时期COVID-19传播的主要途径之一.基于病毒在人群和宿主之间的传播规律以及人口迁移的影响

提出了一类具有迁移效应

无症状感染者和隔离措施的COVID-19传播动力学模型

并利用下一代矩阵方法给出了基本再生数的精确表达式.进一步

利用线性近似和构造Lyapunov函数的方法

证明了当基本再生数小于1时

无感染平衡态是全局渐近稳定的;而当基本再生数大于1时

疾病是一致持久的.数值模拟解释了主要的理论结果并验证了防控措施的可行性.

Abstract

Population flow is one of the main ways of COVID-19 transmission at present and in the future.Based on the law of virus transmission between people and hosts

and the influence of population migration

a kind of COVID-19 transmission dynamic model with migration effect

asymptomatic infection and isolation measures is proposed

and the accurate expression of basic reproduction number is given by using next generation matrix method. Further

by using the method and skill of linear approximation and Lyapunov function

it is proved that when the basic reproduction number is less than 1

the disease-free equilibrium is globally asymptotically stable;when the basic reproduction number is greater than 1

the disease is uniformly persistent. Numerical simulation explains the main theoretical results and verifies the feasibility of the control measures.

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references

CHEN T M, RUI J, WANG Q P, et al. A mathematical model for simulating the phase-based transmissibility of a novel coronavirus[J]. Infectious Diseases of Poverty, 2020, 9:24.

LI Q, GUAN X H, WU P, et al. Early transmission dynamics in Wuhan, China, of novel coronavirus-infected pneumonia[J]. The New England Journal of Medicine, 2020, 382(13):1199-1207.

TANG B, WANG X, LI Q, et al. Estimation of the transmission risk of the 2019-n Co V and its implication for public health interventions[J]. Journal of Clinical Medicine, 2020, 9:462.

SHAO N, ZHONG M, YAN Y, et al. Dynamic models for coronavirus disease 2019 and data analysis[J]. Mathematical Methods in the Applied Sciences, 2020, 43:4943-4949.

BRAUER F, VAN DEN DRIESSCHE P. Model for transmission of disease with immigration of infectives[J]. Mathematical Biosciences, 2001, 171(2):143-154.

WANG W D, MULONE G. Threshold of disease transmission in a patch environment[J]. Journal of Mathematical Analysis and Applications, 2003, 285(1):321-335.

WANG W D. Population dispersal and disease spread[J]. Discrete and Continuous Dynamical Systems-B, 2004, 4:797-804.

WANG W D, ZHAO X Q. An epidemic model in a patchy environment[J]. Mathematical Biosciences, 2004, 190(1):97-112.

李怀阳,张龙.两斑块单向脉冲扩散两种群竞争系统研究[J].新疆大学学报(自然科学版), 2012, 29(3):306-312.

徐高,张龙.两斑块间具有非对称脉冲扩散的带时滞的捕食食饵系统的分析[J].新疆大学学报(自然科学版), 2014, 31(3):280-288.

MARTCHEVA M, ANTMAN S, HOLMES P. An introduction to mathematical epidemiology[M]. Boston:Springer, 2015.

LASALLE J P. The stability of dynamical systems[M]. Philadelphia PA:SIAM, 1976.

SUN C J, YANG W, ARINO J, et al. Effect of media-induced social distancing on disease transmission in a two patch setting[J].Mathematical Biosciences, 2011, 230:87-95.

THIEME H R. Persistence under relaxed point-dissipativity(with application to an endemic model)[J]. SIAM Journal on Mathematical Analysis, 1993, 24:407-435.

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