具有自然年龄和染病年龄的MSIR传染病模型的稳定性

曹志远; 郭俐辉

doi:10.13568/j.cnki.651094.651316.2023.11.16.0002

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具有自然年龄和染病年龄的MSIR传染病模型的稳定性

数理科学 | 更新时间：2026-01-21

- 具有自然年龄和染病年龄的MSIR传染病模型的稳定性
- 具有自然年龄和染病年龄的MSIR传染病模型的稳定性
- 新疆大学学报（自然科学版中英文） 2024年41卷第4期页码：419-426
- 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：
  
  新疆维吾尔自治区自然科学基金“双曲型偏微分方程组初边值问题解的存在性”（2022D01E42）
- DOI：10.13568/j.cnki.651094.651316.2023.11.16.0002
  中图分类号： O175;R181
- 纸质出版：2024
- 稿件说明：
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[1]曹志远,郭俐辉.具有自然年龄和染病年龄的MSIR传染病模型的稳定性[J].新疆大学学报(自然科学版中英文),2024,41(04):419-426.
[1]曹志远,郭俐辉.具有自然年龄和染病年龄的MSIR传染病模型的稳定性[J].新疆大学学报(自然科学版中英文),2024,41(04):419-426. DOI： 10.13568/j.cnki.651094.651316.2023.11.16.0002.

DOI：10.13568/j.cnki.651094.651316.2023.11.16.0002.

摘要

在总人口规模不变的假设下

建立一类具有自然年龄和染病年龄的MSIR传染病模型

并研究该模型平衡解的稳定性.首先

对模型做归一化处理

并在无病平衡解处线性化

证明当R1<1时

无病平衡解是局部渐近稳定的.其次

利用双曲方程组的特征线方法和Fatou引理

证明当R1<1时

无病平衡解是全局渐近稳定的.最后

利用介值定理证明当R1> 1时

模型存在唯一的地方病平衡解.

Abstract

Assuming total population remains constant

this paper establishes a class of MSIR epidemic models with both natural age and infection-age and studies the stability of the equilibrium solutions of this model. Firstly

by normalizing the model and linearizing it at the disease-free equilibrium

demonstrating that when R1< 1

the disease-free equilibrium is locally asymptotically stable. Subsequently

employing the method of characteristics for hyperbolic systems and Fatou's lemma

it is proven that when R1< 1

the disease-free equilibrium is globally asymptotically stable. Finally

the existence of a unique endemic equilibrium solution is established using the intermediate value theorem when R1> 1.

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references

KERMACK W O,MCKENDRICK A G.Contributions to the mathematical theory of epidemics-I[J].Bulletin of Mathematical Biology,1991,53(1):33-55.

SUN D D,TENG Z D,WANG K,et al.Stability and Hopf bifurcation in delayed age-structured SVIR epidemic model with vaccination and incubation[J].Chaos,Solitons&Fractals,2023,168:113206.

HE S B,PENG Y X,SUN K H.SEIR modeling of the COVID-19 and its dynamics[J].Nonlinear Dynamics,2020,101(3):1667-1680.

方彬，杨金根，李学志．潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型的稳定性[J]．应用数学，2009,22(1):90-100.FANG B,YANG J G,LI X Z. Stability of an age-structured MSEIS epidemic model with recovery both in latent period and in infectious period[J].Mathematica Applicata,2009,22(1):90-100.(in Chinese)

ALMEIDA R,BRITO DA CRUZ A M C,MARTINS N,et al.An epidemiological MSEIR model described by the Caputo fractional derivative[J].International Journal of Dynamics and Control,2019,7(2):776-784.

HOPPENSTEADT F.An age dependent epidemic model[J].Journal of the Franklin Institute,1974,297(5):325-333.

LI X Z,GUPUR G,ZHU G T.Threshold and stability results for an age-structured SEIR epidemic model[J].Computers&Mathematics with Applications,2001,42(6/7):883-907.

方彬，蔡礼明，马凌霄．一类带有接种和年龄结构的SVIR传染病模型[J]．生物数学学报，2014,29(2):347-353.FANG B,CAI L M,MA L X.An age-structured SVIR epidemic model with vaccination[J].Journal of Biomathematics,2014,29(2):347-353.(in Chinese)

由守科，闫萍．一类具有潜伏期和染病年龄的SEIR传染病模型[J]．新疆大学学报(自然科学版)，2010,27(3):288-297.YOU S K,YAN P.A class of SEIR epidemic model with latent period and infectious age[J].Journal of Xinjiang University(Natural Science Edition),2010,27(3):288-297.(in Chinese)

由守科，俞芳．一类具有隔离和接种的年龄结构的SIQR传染病模型分析[J]．新疆大学学报(自然科学版)，2013,30(2):177-182.YOU S K,YU F.Analysis of an age-structured SIQR epidemic model with quarantine and vaccination[J].Journal of Xinjiang University(Natural Science Edition),2013,30(2):177-182.(in Chinese)

王时雯，由守科．具有自然年龄和染病年龄的SIQRS传染病模型的稳定性[J]．数学的实践与认识，2022,52(2):163-171.WANG S W,YOU S K.The stability of SIQRS epidemic model with natural age and infection-age[J].Mathematics in Practice and Theory,2022,52(2):163-171.(in Chinese)

王时雯，由守科．具有自然年龄和染病年龄的SIQS传染病模型的稳定性[J]．重庆理工大学学报(自然科学)，2022,36(11):274-281.WANG S W,YOU S K.The stability of SIQS epidemic model with natural age and infection-age[J].Journal of Chongqing University of Technology(Natural Science),2022,36(11):274-281.(in Chinese)

粟丹，赵春．具有垂直传染和年龄结构的MSEIR传染病模型的稳定性[J]．天津师范大学学报(自然科学版)，2020,40(6):9-13+18.SU D,ZHAO C.Stability of an age-structured MSEIR epidemic model with vertical transmission[J].Journal of Tianjin Normal University(Natural Science Edition),2020,40(6):9-13+18.(in Chinese)

LI X Z,GUPUR G,ZHU G T.Existence and uniqueness of endemic states for the age-structured MSEIR epidemic model[J].Acta Mathematicae Applicatae Sinica,2002,18(3):441-454.

陈清江，李学志，代丽霞．带接种疫苗和二次感染的年龄结构MSEIR流行病模型分析[J]．系统科学与数学，2005,25(4):385-397.CHEN Q J,LI X Z,DAI L X.Analysis of an age-structured MSEIR epidemic model with vaccination and the loss of immunity[J].Journal of Systems Science and Mathematical Sciences,2005,25(4):385-397.(in Chinese)

方彬，李学志．潜伏期具有传染性的年龄结构MSEIS流行病模型的稳定性[J]．应用数学学报，2008,31(1):110-125.FANG B,LI X Z.Stability of an age-structured MSEIS epidemic model with infectivity in latent period[J].Acta Mathematicae Applicatae Sinica,2008,31(1):110-125.(in Chinese)

WEBB G F.Theory of nonlinear age-dependent population dynamics[M].New York:Marcel Dekker,1985.

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