• 论文 •

### 具有年龄结构的麻疹传染病模型的稳定性分析

1. 1 新疆农业大学数理学院 乌鲁木齐 830052
2 新疆大学数学与系统科学学院 乌鲁木齐 830046
3 长安大学理学院 西安 710064
• 收稿日期:2020-07-03 出版日期:2021-12-26 发布日期:2021-12-02
• 通讯作者: 孙丹丹 E-mail:dandan_1990@126.com;307129154@qq.com
• 作者简介:李盈科, E-mail: 307129154@qq.com
• 基金资助:
中国博士后科学基金资助项目(2020M683714XB);新疆维吾尔自治区自然科学计划（自然科学基金）面上项目(2021D01A98);陕西省自然科学基础研究计划项目(2021JM-445)

### Analysis of the Stability for Measles Epidemic Model with Age-Structured

Dandan Sun1,*(),Yingke Li1(),Zhidong Teng2,Tailei Zhang3

1. 1 School of Mathematics and Physics, Xinjiang Agriculture University, Urumqi 830052
2 School of Mathematics and System Science, Xinjiang University, Urumqi 830046
3 School of Sciences, Changan University, Xi an 710064
• Received:2020-07-03 Online:2021-12-26 Published:2021-12-02
• Contact: Dandan Sun E-mail:dandan_1990@126.com;307129154@qq.com
• Supported by:
the China Postdoctoral Science Foundation(2020M683714XB);the NSF of Xinjiang(2021D01A98);the Natural Science Basic Research Plan in Shaanxi Province(2021JM-445)

Abstract:

In this paper, a kind of SVEIR measles epidemic model with age structure is established. Firstly, the model is transformed into Volterra integral equation and the well-possdness of solutions of the model is obtained, including non-negativity, boundedness, asymptotic smoothness, etc. Then the equilibria and the basic reproduction number ${{\cal R}}_{0}$ of the model is derived, and it is proved that the epidemic is uniformly persistent when ${{\cal R}}_{0}>1$. Further by analyzing the characteristic equations and selecting suitable Lyapunov functions, we get the model only has the disease-free equilibrium that is globally asymptotically stable if ${{\cal R}}_{0}<1$; if ${{\cal R}}_{0}>1$, the disease-free equilibrium is unstable, the endemic disease equilibrium exist and is globally asymptotically stable. These main theoretical results are applied in the analysis of the trend in data on measles infectious diseases across the country.

• O175.1