Stability analysis of MSIQRS epidemiological model with age structure

DOU Zhongli

doi:10.13471/j.cnki.acta.snus.2019.09.20.2019A071

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Stability analysis of MSIQRS epidemiological model with age structure

Research articles | 更新时间：2023-12-08

- Stability analysis of MSIQRS epidemiological model with age structure
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 60, Issue 3, Pages: 159-166(2021)
- 作者机构：
  
  重庆财经学院，重庆 400055
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2019.09.20.2019A071
  CLC： O175.12
- Published：25 May 2021，
  
  Published Online：05 November 2020，
  
  Received：20 September 2019，
  
  Accepted：18 September 2020
扫描看全文
豆中丽.具有年龄结构的MSIQRS传染病模型的稳定性分析[J].中山大学学报(自然科学版),2021,60(03):159-166.

DOU Zhongli.Stability analysis of MSIQRS epidemiological model with age structure[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(03):159-166.
豆中丽.具有年龄结构的MSIQRS传染病模型的稳定性分析[J].中山大学学报(自然科学版),2021,60(03):159-166. DOI： 10.13471/j.cnki.acta.snus.2019.09.20.2019A071.

DOU Zhongli.Stability analysis of MSIQRS epidemiological model with age structure[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(03):159-166. DOI： 10.13471/j.cnki.acta.snus.2019.09.20.2019A071.

摘要

讨论一类具有年龄结构MSIQRS传染病模型，得出基本再生数

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147669&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147667&type=

3.04800010

3.21733332

和接种再生数

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147671&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147681&type=

6.60400009

2.96333337

的表达式，证明了当

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147687&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147685&type=

11.93799973

2.96333337

时，无病平衡点局部渐近稳定；当

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147692&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147689&type=

8.72066593

3.21733332

时，无病平衡点全局渐近稳定性；当

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147708&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147694&type=

11.93799973

2.96333337

时，无病平衡点不稳定，此时系统存在地方病平衡点，并给出了地方病平衡点局部渐近稳定的条件；同时用基本再生数的表达式进一步解释了接种在控制消除传染病中的作用。

Abstract

A class of MSIQRS epidemic models with age structure was discussed， and the expressions of basic reproductive number

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147709&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51147698&type=

3.47133350

3.72533321

and the reproductive number with vaccination

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149215&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149230&type=

7.70466709

3.47133350

were derived. It was proved that when

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149187&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149199&type=

13.88533401

3.47133350

， the disease-free equilibrium was locally asymptotically stable at that time.when

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149218&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149204&type=

9.99066734

3.80999994

，the disease-free equilibrium was globally asymptotically stable. When

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149221&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=51149207&type=

13.88533401

3.47133350

， the disease-free equilibrium is unstable. And there exists only endemic equilibrium state， and the conditions of local asymptotic stability of the endemic equilibrium point are given. The expression of basic reproductive number is used to further explain the role of isolation in the control of eliminating infectious diseases.

关键词

年龄结构接种基本再生数稳定性

Keywords

age structurevaccinationbasic reproductive numberstability

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王改霞，刘纪轩，李学志.年龄结构SIQR传染病模型及稳定性［J］.应用数学学报，2018，41（6）： 777-787.

WANG G X，LIU J X，LI X Z.Stability of age-structured SIQR epidemiological model ［J］. Acta Mathematicae Applicatae Sinica，2018，41（6）： 777-787.

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