在线阅读 --自然科学版 2020年5期《具有年龄结构的SEIR传染病模型的定性分析》
具有年龄结构的SEIR传染病模型的定性分析--[在线阅读]
孙丹丹
新疆农业大学 数理学院, 新疆 乌鲁木齐 830052
起止页码: 380--389页
DOI: 10.13763/j.cnki.jhebnu.nse.2020.05.003
摘要
建立了一类具有年龄结构的SEIR传染病模型.将模型重新化成Volterra型积分方程,得到模型的基本再生数R0,并证明了该模型解半流的存在唯一性、有界性、渐近光滑性,通过分析特征方程和构造适当的Lyapunov函数,证明了平衡点的局部稳定性和全局稳定性.最后进行数值模拟,探索了年龄分布对潜伏仓室、恢复仓室进入感染仓室的影响,并绘制热图研究β,μ对疾病消亡或爆发的影响.

Qualitative Analysis of an SEIR Epidemic Model with Age-dependent
SUN Dandan
College of Mathematics and Science, Xinjiang Agricultural University, Xinjiang Urumqi 830052, China
Abstract:
In this paper, an SEIR epidemic model with age-dependent is investigated.The existence,uniqueness,boundedness and asymptotic smoothness are proved by reformulating it as the Volterra integral equation,and obtaining the basic reproduction number R0.By analysing the characteristic equations and constructing the suitable Lyapunov function,the local stability and global stability of the equilibrium point are proved.Finally,the numerical simulation is developed to explore the influence of age distribution on the entry of the latency and recovery compartments into infection compartments,and the thermal map is drawn to study the effect of β,μ on the disappearance or outbreak of disease.

收稿日期: 2020-03-08
基金项目: 新疆维吾尔自治区高校科研项目(XJEDU2018Y021)

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