Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network

A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Fu...

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Main Authors: Zizhen Zhang, Huizhong Yang
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2013/319174
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spelling doaj-0417bf09237049618cb15848d12363a62020-11-25T00:11:25ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/319174319174Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer NetworkZizhen Zhang0Huizhong Yang1Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, ChinaKey Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, ChinaA delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.http://dx.doi.org/10.1155/2013/319174
collection DOAJ
language English
format Article
sources DOAJ
author Zizhen Zhang
Huizhong Yang
spellingShingle Zizhen Zhang
Huizhong Yang
Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
Mathematical Problems in Engineering
author_facet Zizhen Zhang
Huizhong Yang
author_sort Zizhen Zhang
title Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
title_short Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
title_full Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
title_fullStr Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
title_full_unstemmed Stability and Hopf Bifurcation in a Delayed SEIRS Worm Model in Computer Network
title_sort stability and hopf bifurcation in a delayed seirs worm model in computer network
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2013-01-01
description A delayed SEIRS epidemic model with vertical transmission in computer network is considered. Sufficient conditions for local stability of the positive equilibrium and existence of local Hopf bifurcation are obtained by analyzing distribution of the roots of the associated characteristic equation. Furthermore, the direction of the local Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by using the normal form theory and center manifold theorem. Finally, a numerical example is presented to verify the theoretical analysis.
url http://dx.doi.org/10.1155/2013/319174
work_keys_str_mv AT zizhenzhang stabilityandhopfbifurcationinadelayedseirswormmodelincomputernetwork
AT huizhongyang stabilityandhopfbifurcationinadelayedseirswormmodelincomputernetwork
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