分数阶时滞SEIR传染病模型的动力学分析
Dynamics Analysis of SEIR Epidemic Model with Fractional Order Time-Delay
豆中丽1
作者信息
- 1. 重庆财经学院软件学院,重庆 401320
- 折叠
摘要
针对具有logistic增长和非线性发生率的分数阶时滞SEIR传染病模型进行研究.利用第二代再生矩阵法计算出模型的基本再生数R0;当R0＜1时,证明无病平衡点是局部渐近稳定的;当R0＞1时,证明时滞情况下地方病平衡点是局部渐近稳定的;选取时滞作为分岔参数,证明地方病平衡点发生Hopf分岔的条件;最后,运用数值模拟验证理论结果的正确性.
Abstract
In this paper,we investigate the fractional order time-delay SEIR epidemic model with logistic growth and nonlinear incidence.Using the second generation regeneration matrix method,we calculate the basic reproduction number Ro of the model.The result indicates that the disease-free equilibrium point possesses the locally asymptotically stability When R0＜1,the sufficient conditions for the existence of backware bifurcation are proved by the center manifold theorem;and the endemic equilibrium point with time delay τ=0 possesses the local asymptotic stability when R0＞1.Taking the time delay as a bifurcation parameter,The condition of Hopf bifurcation in endemic equilibrium point is proved by using the bifurcation theory,Finally,the correctness of theoretical analysis is verified by numerical simulations.
关键词
Hopf分岔/稳定性/分数阶/时滞Key words
Hopf bifurcation/stability/fractional order/delay引用本文复制引用
基金项目
国家自然科学基金(11304403)
重庆市教委科技创新项目(KJQN201902105)
出版年
2024
NETL
NSTL
万方数据