Hopf bifurcation of an SEIRS epidemic model with delays and vertical transmission in the network

Advances in Difference Equations

Chunlei Wang¹  Shouxia Chai² 

[1] Network Center, Hubei University of Medicine, Shiyan, P.R. China;Nursing College, Hubei University of Medicine, Shiyan, P.R. China

关键词: Hopf bifurcation;    delay;    SEIRS model;    stability;    periodic solution;   

DOI  :  10.1186/s13662-016-0793-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

An SEIRS worm propagation model with two delays and vertical transmission in the network is investigated. It is proved that the positive equilibrium is locally asymptotically stable and the Hopf bifurcation can occur when the certain conditions are satisfied by regarding different combination of the two delays as bifurcation parameter. Then the properties of the Hopf bifurcation, such as direction and stability, are studied by using the normal form theory and the center manifold theorem. Finally, some numerical simulations are presented to verify the obtained results and to demonstrate the dynamics of the model.

【 授权许可】

CC BY