Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay

In this paper, first a third degree transcendental polynomial is studied and the distribution of its zeros is established. Then the results are applied to study an SEIR model with a time delay. We show that, under some conditions, as the time delay increases, a stable endemic equilibrium will beco...

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Main Authors:	Liancheng Wang, Xiaoqin Wu
Format:	Article
Language:	English
Published:	ATNAA 2018-07-01
Series:	Advances in the Theory of Nonlinear Analysis and its Applications
Subjects:	Transcendental polynomial SEIR model Hopf bifurcation
Online Access:	http://dergipark.gov.tr/download/article-file/594208

id	doaj-023364cf41924737942215dfd7ea0a68
record_format	Article
spelling	doaj-023364cf41924737942215dfd7ea0a682020-11-25T00:03:38ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482587-26482018-07-012311312710.31197/atnaa.380970Stability and Hopf Bifurcation for an SEIR Epidemic Model with DelayLiancheng Wang0Xiaoqin Wu1aDepartment of Mathematics, Kennesaw State University, Marietta, GA 30060, USADepartment of Mathematics, Computer and Information Sciences, Mississippi Valley State University, Itta Bena, MS 39762, USAIn this paper, first a third degree transcendental polynomial is studied and the distribution of its zeros is established. Then the results are applied to study an SEIR model with a time delay. We show that, under some conditions, as the time delay increases, a stable endemic equilibrium will become unstable and periodic solution emerges by Hopf bifurcation. By finding the normal form of the system, the direction and the stability of the periodic solution are established. Numerical simulations are performed to demonstrate the theoretical results. http://dergipark.gov.tr/download/article-file/594208Transcendental polynomialSEIR modelHopf bifurcation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Liancheng Wang Xiaoqin Wu
spellingShingle	Liancheng Wang Xiaoqin Wu Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay Advances in the Theory of Nonlinear Analysis and its Applications Transcendental polynomial SEIR model Hopf bifurcation
author_facet	Liancheng Wang Xiaoqin Wu
author_sort	Liancheng Wang
title	Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay
title_short	Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay
title_full	Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay
title_fullStr	Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay
title_full_unstemmed	Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay
title_sort	stability and hopf bifurcation for an seir epidemic model with delay
publisher	ATNAA
series	Advances in the Theory of Nonlinear Analysis and its Applications
issn	2587-2648 2587-2648
publishDate	2018-07-01
description	In this paper, first a third degree transcendental polynomial is studied and the distribution of its zeros is established. Then the results are applied to study an SEIR model with a time delay. We show that, under some conditions, as the time delay increases, a stable endemic equilibrium will become unstable and periodic solution emerges by Hopf bifurcation. By finding the normal form of the system, the direction and the stability of the periodic solution are established. Numerical simulations are performed to demonstrate the theoretical results.
topic	Transcendental polynomial SEIR model Hopf bifurcation
url	http://dergipark.gov.tr/download/article-file/594208
work_keys_str_mv	AT lianchengwang stabilityandhopfbifurcationforanseirepidemicmodelwithdelay AT xiaoqinwu stabilityandhopfbifurcationforanseirepidemicmodelwithdelay
_version_	1725432760676384768

Stability and Hopf Bifurcation for an SEIR Epidemic Model with Delay

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