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

作　　者：豆中丽 DOU Zhong-li(School of Software,Chongqing Finance and Economics College,Chongqing 401320,China)

机构地区：[1]重庆财经学院软件学院,重庆401320

出　　处：《数学的实践与认识》2024年第4期162-170,共9页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11304403);重庆市教委科技创新项目(KJQN201902105)。

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.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 Ro<1,the suficient conditions for the existence of backware bifurcation are proved by the center manifold theorem;and the endemic equilibrium point with time delay T=O possesses the local asymptotic stability when Ro>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 

分 类 号：O175[理学—数学] R181[理学—基础数学]