Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence

This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choo...

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Main Authors: Zizhen Zhang, Yougang Wang, Luca Guerrini
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/7619074
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spelling doaj-0a23d57bb7a54f78996c8b8b91ed56492021-07-02T05:48:46ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/76190747619074Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated IncidenceZizhen Zhang0Yougang Wang1Luca Guerrini2School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaSchool of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, ChinaDepartment of Management, Marche Polytechnic University, Piazza Martelli 8, 60121 Ancona, ItalyThis paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results.http://dx.doi.org/10.1155/2018/7619074
collection DOAJ
language English
format Article
sources DOAJ
author Zizhen Zhang
Yougang Wang
Luca Guerrini
spellingShingle Zizhen Zhang
Yougang Wang
Luca Guerrini
Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence
Advances in Mathematical Physics
author_facet Zizhen Zhang
Yougang Wang
Luca Guerrini
author_sort Zizhen Zhang
title Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence
title_short Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence
title_full Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence
title_fullStr Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence
title_full_unstemmed Bifurcation Analysis of a Delayed Worm Propagation Model with Saturated Incidence
title_sort bifurcation analysis of a delayed worm propagation model with saturated incidence
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
description This paper is concerned with a delayed SVEIR worm propagation model with saturated incidence. The main objective is to investigate the effect of the time delay on the model. Sufficient conditions for local stability of the positive equilibrium and existence of a Hopf bifurcation are obtained by choosing the time delay as the bifurcation parameter. Particularly, explicit formulas determining direction of the Hopf bifurcation and stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold theorem. Numerical simulations for a set of parameter values are carried out to illustrate the analytical results.
url http://dx.doi.org/10.1155/2018/7619074
work_keys_str_mv AT zizhenzhang bifurcationanalysisofadelayedwormpropagationmodelwithsaturatedincidence
AT yougangwang bifurcationanalysisofadelayedwormpropagationmodelwithsaturatedincidence
AT lucaguerrini bifurcationanalysisofadelayedwormpropagationmodelwithsaturatedincidence
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