Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R0, and we prove, a Lyapunov function, that for R0<1the drug-free equilibrium is globally as...

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Autores principales:	Salih Djilali, Soufiane Bentout, Tarik Mohammed Touaoula, Abdessamad Tridane, Sunil Kumar
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Lyapunov functional Uniform persistence Weak delay Global stability Physics QC1-999
Acceso en línea:	https://doaj.org/article/71bf8a3d3d38410bbb71fa52f0829253
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spelling	oai:doaj.org-article:71bf8a3d3d38410bbb71fa52f08292532021-11-18T04:48:12ZGlobal behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function2211-379710.1016/j.rinp.2021.104953https://doaj.org/article/71bf8a3d3d38410bbb71fa52f08292532021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2211379721009712https://doaj.org/toc/2211-3797In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R0, and we prove, a Lyapunov function, that for R0<1the drug-free equilibrium is globally asymptotically stable. For R0>1, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R0>1using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.Salih DjilaliSoufiane BentoutTarik Mohammed TouaoulaAbdessamad TridaneSunil KumarElsevierarticleLyapunov functionalUniform persistenceWeak delayGlobal stabilityPhysicsQC1-999ENResults in Physics, Vol 31, Iss , Pp 104953- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Lyapunov functional Uniform persistence Weak delay Global stability Physics QC1-999
spellingShingle	Lyapunov functional Uniform persistence Weak delay Global stability Physics QC1-999 Salih Djilali Soufiane Bentout Tarik Mohammed Touaoula Abdessamad Tridane Sunil Kumar Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function
description	In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R0, and we prove, a Lyapunov function, that for R0<1the drug-free equilibrium is globally asymptotically stable. For R0>1, we give the persistence result of the heroin consumption. We also show the global stability of the endemic equilibrium for R0>1using a suitable Lyapunov function. The mathematical results are illustrated by numerically simulations.
format	article
author	Salih Djilali Soufiane Bentout Tarik Mohammed Touaoula Abdessamad Tridane Sunil Kumar
author_facet	Salih Djilali Soufiane Bentout Tarik Mohammed Touaoula Abdessamad Tridane Sunil Kumar
author_sort	Salih Djilali
title	Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function
title_short	Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function
title_full	Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function
title_fullStr	Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function
title_full_unstemmed	Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function
title_sort	global behavior of heroin epidemic model with time distributed delay and nonlinear incidence function
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/71bf8a3d3d38410bbb71fa52f0829253
work_keys_str_mv	AT salihdjilali globalbehaviorofheroinepidemicmodelwithtimedistributeddelayandnonlinearincidencefunction AT soufianebentout globalbehaviorofheroinepidemicmodelwithtimedistributeddelayandnonlinearincidencefunction AT tarikmohammedtouaoula globalbehaviorofheroinepidemicmodelwithtimedistributeddelayandnonlinearincidencefunction AT abdessamadtridane globalbehaviorofheroinepidemicmodelwithtimedistributeddelayandnonlinearincidencefunction AT sunilkumar globalbehaviorofheroinepidemicmodelwithtimedistributeddelayandnonlinearincidencefunction
_version_	1718425045711192064

Global behavior of Heroin epidemic model with time distributed delay and nonlinear incidence function

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