Stability and hopf bifurcation on an SEIR delayed model with logistic growth

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Author list: Sirijampa A., Chinviriyasit S., Chinviriyasit W.

Publisher: Prince of Songkla University

Publication year: 2018

Journal: Songklanakarin Journal of Science and Technology (SJST) (0125-3395)

Volume number: 40

Issue number: 4

Start page: 928

End page: 952

Number of pages: 25

ISSN: 0125-3395

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85057178272&doi=10.14456%2fsjst-psu.2018.118&partnerID=40&md5=fa3226113f3619797fa13d962e556ccc

Languages: English-Great Britain (EN-GB)

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Abstract

This paper investigates the stability and Hopf bifurcation of SEIR delay model with logistic growth. Firstly, the existence and uniqueness of equilibrium point are analyzed. For the study of the stability of the equilibrium point time delay () was chosen as the bifurcation parameter. By considering the roots of characteristic equations, it was found that disease-free equilibrium is locally asymptotically stable for all τ ≥ 0 . The endemic equilibrium of the model is conditionally stable. Hopf bifurcation will occur when the bifurcation parameter passes through a critical value. Moreover, stability and direction of Hopf bifurcation are obtained by using the normal form theory and the center manifold reduction. Finally, the numerical solutions are simulated to verify the theoretical results. © 2018, Prince of Songkla University. All rights reserved.

Keywords

Hopf bifurcation, Local stability, Logistic growth, SEIR model, Time delay