具有双线性发生率的SEIR模型的Hopf分支分析  

Analysis of the Hopf Bifurcation of the SEIR Model with the Bilinear Incidence Rate

作　　者：豆中丽 DOU Zhongli(Chongqing Finance and Economics College,Chongqing,401320 China)

机构地区：[1]重庆财经学院,重庆401320

出　　处：《科技资讯》2024年第11期246-248,253,共4页Science & Technology Information

基　　金：重庆市教委科技创新项目(项目编号:KJQN201902105)。

摘　　要：讨论具有双线性发生率的SEIR模型的Hopf分支,首先通过计算得到模型的基本再生数和疾病持续存在的地方病平衡点;将系统线性化,选取适当的参数β*,利用中心流形定理和规范性证明在地方病平衡点处存在生Hopf分支,并得到相应Hopf分支产生的充分条件;当第一Lyapunov系数l1(0)<0时,在地方病平衡点附近有超临界的Hopf分支产生。This paper discusses the Hopf bifurcation of the SEIR model with the bilinear incidence rate.Firstly,it obtains the basic reproductive number of the model and an endemic equilibrium point of disease persistence by cal⁃culating.Then,it linearizes the system,selects appropriate parameters,proves the existence of the Hopf bifurcation at the endemic equilibrium point by the central manifold theorem and the normal form,and obtains sufficient con⁃ditions for the generation of the corresponding Hopf bifurcation.When the first Lyapunov coefficient l1(0)<0,there is the supercritical Hopf bifurcation near the endemic equilibrium point.

关 键 词：基本再生数 HOPF分支 中心流形定理 双线性发生率 

分 类 号：O175.13[理学—数学]