具有自然年龄和染病年龄的MSIR传染病模型的稳定性
The Stability of MSIR Epidemic Model with Natural Age and Infection-Age
曹志远 1郭俐辉1
作者信息
- 1. 新疆大学数学与系统科学学院,新疆乌鲁木齐 830017
- 折叠
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
MSIR传染病模型/染病年龄/平衡解/存在性Key words
MSIR epidemic model/infection-age/equilibrium solution/existence引用本文复制引用
基金项目
新疆维吾尔自治区自然科学基金(2022D01E42)
出版年
2024
国家科技期刊平台
NSTL
万方数据