具有垂直传染和年龄结构的MSEIR传染病模型的稳定性  

Stability of an age-structured MSEIR epidemic model with vertical transmission

作　　者：粟丹 赵春[1] SU Dan;ZHAO Chun(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《天津师范大学学报（自然科学版）》2020年第6期9-13,18,共6页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市高等学校创新团队培养计划资助项目(TD13-5078).

摘　　要：讨论一类具有年龄结构和垂直传染的传染病模型的稳定性问题.利用不动点定理证明了模型非负解的存在唯一性.通过归一化证明了无病平衡点的存在性,利用特征方程得到基本再生数R0的表达式,证明了当R0<1时,无病平衡点局部渐近稳定,当R0>1时,无病平衡点不稳定.The stability of an epidemic model with age structure and vertical transmission is discussed.The existence and uniqueness of the non-negative solutions of the model are proved by a fixed point theorem.The existence of the disease-free equilibrium point is proved by normalization.The expression of the basic reproduction number R0 is obtained by using the characteristic equation.It is proved that when R0<1,the disease-free equilibrium point is locally asymptotically stable,and when R0>1,the disease-free equilibrium point is unstable.

关 键 词：年龄结构 垂直传染 平衡点 基本再生数 

分 类 号：O175[理学—数学]