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

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
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 41, Issue 4, Pages: 419-426(2024)
- 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：
- DOI：10.13568/j.cnki.651094.651316.2023.11.16.0002
  CLC： O175;R181
- Published：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.

关键词

Keywords

references

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