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
豆中丽1
作者信息
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.
Abstract
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Key words
Basic reproductive number/Hopf bifurcation/Central manifold theorem/Bilinear incidence rate引用本文复制引用
基金项目
重庆市教委科技创新项目(KJQN201902105)
出版年
2024
NETL
NSTL
万方数据