Global dynamics of alcoholism epidemic model with distributed delays

This paper aims to investigate the global dynamics of an alcoholism epidemic model with distributed delays. The main feature of this model is that it includes the effect of the social pressure as a factor of drinking. As a result, our global stability is obtained without a "basic reproduction n...

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Autores principales:	Salih Djillali, Soufiane Bentout, Tarik Mohammed Touaoula, Abdessamad Tridane
Formato:	article
Lenguaje:	EN
Publicado:	AIMS Press 2021
Materias:	alcoholism model lyapunov direct method global stability Biotechnology TP248.13-248.65 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/e972e8e11c5e44c8b3b9952631ab652c
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id	oai:doaj.org-article:e972e8e11c5e44c8b3b9952631ab652c
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spelling	oai:doaj.org-article:e972e8e11c5e44c8b3b9952631ab652c2021-11-24T01:11:15ZGlobal dynamics of alcoholism epidemic model with distributed delays10.3934/mbe.20214091551-0018https://doaj.org/article/e972e8e11c5e44c8b3b9952631ab652c2021-09-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021409?viewType=HTMLhttps://doaj.org/toc/1551-0018This paper aims to investigate the global dynamics of an alcoholism epidemic model with distributed delays. The main feature of this model is that it includes the effect of the social pressure as a factor of drinking. As a result, our global stability is obtained without a "basic reproduction number" nor threshold condition. Hence, we prove that the alcohol addiction will be always uniformly persistent in the population. This means that the investigated model has only one positive equilibrium, and it is globally asymptotically stable independent on the model parameters. This result is shown by proving that the unique equilibrium is locally stable, and the global attraction is shown using Lyapunov direct method.Salih DjillaliSoufiane BentoutTarik Mohammed TouaoulaAbdessamad TridaneAIMS Pressarticlealcoholism modellyapunov direct methodglobal stabilityBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 6, Pp 8245-8256 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	alcoholism model lyapunov direct method global stability Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	alcoholism model lyapunov direct method global stability Biotechnology TP248.13-248.65 Mathematics QA1-939 Salih Djillali Soufiane Bentout Tarik Mohammed Touaoula Abdessamad Tridane Global dynamics of alcoholism epidemic model with distributed delays
description	This paper aims to investigate the global dynamics of an alcoholism epidemic model with distributed delays. The main feature of this model is that it includes the effect of the social pressure as a factor of drinking. As a result, our global stability is obtained without a "basic reproduction number" nor threshold condition. Hence, we prove that the alcohol addiction will be always uniformly persistent in the population. This means that the investigated model has only one positive equilibrium, and it is globally asymptotically stable independent on the model parameters. This result is shown by proving that the unique equilibrium is locally stable, and the global attraction is shown using Lyapunov direct method.
format	article
author	Salih Djillali Soufiane Bentout Tarik Mohammed Touaoula Abdessamad Tridane
author_facet	Salih Djillali Soufiane Bentout Tarik Mohammed Touaoula Abdessamad Tridane
author_sort	Salih Djillali
title	Global dynamics of alcoholism epidemic model with distributed delays
title_short	Global dynamics of alcoholism epidemic model with distributed delays
title_full	Global dynamics of alcoholism epidemic model with distributed delays
title_fullStr	Global dynamics of alcoholism epidemic model with distributed delays
title_full_unstemmed	Global dynamics of alcoholism epidemic model with distributed delays
title_sort	global dynamics of alcoholism epidemic model with distributed delays
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/e972e8e11c5e44c8b3b9952631ab652c
work_keys_str_mv	AT salihdjillali globaldynamicsofalcoholismepidemicmodelwithdistributeddelays AT soufianebentout globaldynamicsofalcoholismepidemicmodelwithdistributeddelays AT tarikmohammedtouaoula globaldynamicsofalcoholismepidemicmodelwithdistributeddelays AT abdessamadtridane globaldynamicsofalcoholismepidemicmodelwithdistributeddelays
_version_	1718416067444867072

Global dynamics of alcoholism epidemic model with distributed delays

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