一个传染病模型的Bogdanov-Takens分支分析(英文)  

Bogdanov-Takens Bifurcation Analysis of an Epidemic Model

作　　者：万辉[1] 李永凤[2] 

机构地区：[1]江苏省大规模复杂系统数值模拟重点实验室,南京师范大学数学科学学院,江苏南京210023 [2]郑州轻工业大学数学与信息科学系,河南郑州450000

出　　处：《南京师大学报（自然科学版）》2012年第4期7-13,共7页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：Supported by NSFC(11126049,11201236,11201433);NSF of the Jiangsu Higher Education Committee of China(11KJA110001,12KJB110012);NSF of Henan(112300410156,2011A110022)

摘　　要：为了研究有限的医疗资源对传染病传播影响,本文考虑了一个SIR传染病模型,并着重分析了模型的Bogdanov-Takens分支问题.结果表明,当基本再生数等于一个子阈值时,模型将出现非常复杂的分支现象.此时,模型惟一的平衡点为余维2尖点.In this paper, a SIR epidemic model is proposed to understand the impact of limited medical resource on infectious disease transmission, and Bogdanov-Takens bifurcation is analyzed. Our results suggest that the model may exhibit vital dynamics when the basic reproduction number H0 is equal to a subthreshold value and the unique equilibrium is a cusp of codimension 2.

关 键 词：传染病模型 医疗资源 Bogdanov—Takens分支 余维2 

分 类 号：O175.12[理学—数学]