On qualitative analysis of a discrete time SIR epidemical model

The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete classification of the systems bifurcations, in particular, a...

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Autores principales:	J. Hallberg Szabadváry, Y. Zhou
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Discrete time SIR epidemic model Stability Fixed points n-cycles Limit cycles Flip bifurcation Physics QC1-999 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1cfbf91f849144b79e175cd398de20cf
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spelling	oai:doaj.org-article:1cfbf91f849144b79e175cd398de20cf2021-11-20T05:12:57ZOn qualitative analysis of a discrete time SIR epidemical model2590-054410.1016/j.csfx.2021.100067https://doaj.org/article/1cfbf91f849144b79e175cd398de20cf2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2590054421000129https://doaj.org/toc/2590-0544The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete classification of the systems bifurcations, in particular, a complete analysis on local stability and codimension 1 bifurcations in the parameter space. Sufficient conditions for positive trajectories are given. The existence of a 3-cycle is shown, which implies the existence of cycles of arbitrary length by the celebrated Sharkovskii’s theorem. Generacity of some bifurcations is examined both analytically and through numerical computations. Bifurcation diagrams along with numerical simulations are presented. The system turns out to have both rich and interesting dynamics.J. Hallberg SzabadváryY. ZhouElsevierarticleDiscrete time SIR epidemic modelStabilityFixed pointsn-cyclesLimit cyclesFlip bifurcationPhysicsQC1-999MathematicsQA1-939ENChaos, Solitons & Fractals: X, Vol 7, Iss , Pp 100067- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Discrete time SIR epidemic model Stability Fixed points n-cycles Limit cycles Flip bifurcation Physics QC1-999 Mathematics QA1-939
spellingShingle	Discrete time SIR epidemic model Stability Fixed points n-cycles Limit cycles Flip bifurcation Physics QC1-999 Mathematics QA1-939 J. Hallberg Szabadváry Y. Zhou On qualitative analysis of a discrete time SIR epidemical model
description	The main purpose of this paper is to study the local dynamics and bifurcations of a discrete-time SIR epidemiological model. The existence and stability of disease-free and endemic fixed points are investigated along with a fairly complete classification of the systems bifurcations, in particular, a complete analysis on local stability and codimension 1 bifurcations in the parameter space. Sufficient conditions for positive trajectories are given. The existence of a 3-cycle is shown, which implies the existence of cycles of arbitrary length by the celebrated Sharkovskii’s theorem. Generacity of some bifurcations is examined both analytically and through numerical computations. Bifurcation diagrams along with numerical simulations are presented. The system turns out to have both rich and interesting dynamics.
format	article
author	J. Hallberg Szabadváry Y. Zhou
author_facet	J. Hallberg Szabadváry Y. Zhou
author_sort	J. Hallberg Szabadváry
title	On qualitative analysis of a discrete time SIR epidemical model
title_short	On qualitative analysis of a discrete time SIR epidemical model
title_full	On qualitative analysis of a discrete time SIR epidemical model
title_fullStr	On qualitative analysis of a discrete time SIR epidemical model
title_full_unstemmed	On qualitative analysis of a discrete time SIR epidemical model
title_sort	on qualitative analysis of a discrete time sir epidemical model
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/1cfbf91f849144b79e175cd398de20cf
work_keys_str_mv	AT jhallbergszabadvary onqualitativeanalysisofadiscretetimesirepidemicalmodel AT yzhou onqualitativeanalysisofadiscretetimesirepidemicalmodel
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On qualitative analysis of a discrete time SIR epidemical model

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