Propagation dynamics of fractional order delay epidemic model

被引：0
|
作者：
Chen G. [1 ]
Xiao M. [1 ]
Wan Y.-H. [1 ]
Wang X.-L. [1 ]
机构：
[1] College of Automation & College of Artificial Intelligence, Nanjing University of Posts and Telecommunications, Nanjing
来源：
Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2021年 / 38卷 / 08期
基金：
中国国家自然科学基金;
关键词：
Fractional order; Hopf bifurcation; SEIR epidemic model; Time delay;
D O I：
10.7641/CTA.2021.00747
中图分类号：
学科分类号：
摘要：
In this paper, a fractional order SEIR epidemic model with time delay is investigated, and the effect of time delay on the dynamic behaviour of the model is investigated. Firstly, the fractional SEIR epidemic model is established and sufficient conditions for the stability of endemic equilibrium point without delay are given to ensure the practical significance of the introduction of time delay. Based on the bifurcation theory, the condition of the Hopf bifurcation and the expression of the bifurcation threshold are obtained. As it turns out, the dynamic behaviors of the system depend on the critical value of the bifurcation. On this basis, the influence of the fractional order on the bifurcation threshold is studied. It is found that the Hopf bifurcation of the system will advance as the order increases. Finally, the accuracy of the theoretical derivation is verified by numerical simulation results. © 2021, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.
引用
收藏
页码：1257 / 1264
页数：7
相关论文
共 36 条
  • [1] SHI Yaolin, Dynamic stochastic model of SARS epidemic diffusion, Chinese Science Bulletin, 48, 13, pp. 1373-1377, (2003)
  • [2] SHAO Nian, CHEN Yu, CHENG Jin, Et al., Some novel statistical time delay dynamic model by statistics data from CDC on novel coronavirus pneumonia, Control Theory & Applications, 37, 4, pp. 697-704, (2020)
  • [3] KERMACK W O, MCKENDRICK A G., A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 115, 772, pp. 700-721, (1927)
  • [4] ZHANG Y, LI Y X., Evolutionary dynamics of stochastic SEIR models with migration and human awareness in complex networks, Complexity, 2020, pp. 1-15, (2020)
  • [5] DIAZ P, CONSTANTINE P, KALMBACH K, Et al., A modified SEIR model for the spread of Ebola in Western Africa and metrics for resource allocation, Applied Mathematics and Computation, 324, pp. 141-155, (2018)
  • [6] TIAN B C, YUAN R., Traveling waves for a diffusive SEIR epidemic model with standard incidences, Science China Mathematics, 60, 5, pp. 813-832, (2017)
  • [7] CHEN Y, CHENG J, JIANG Y, Et al., A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification, Journal of Inverse and Ill-posed Problems, 28, 2, pp. 243-250, (2020)
  • [8] XU C H, YU Y G, CHEN Y Q, Et al., Forecast analysis of the epidemics trend of COVID-19 in the USA by a generalized fractionalorder SEIR model, Nonlinear Dynamics, 101, pp. 1621-1634, (2020)
  • [9] WEI G, VEERESHA P, PRAKASHA D G, Et al., Novel dynamic structures of 2019-nCoV with nonlocal operator via powerful computational technique, Biology, 9, 5, (2020)
  • [10] ZHAO Xuan, LI Baogen, YU Zuguo, Study on the SEIS and SEIR models on scale-free networks and dynamic small-world networks, Natural Science Journal of Xiangtan University, 40, 1, pp. 58-62, (2018)
1234