An efficient computational analysis for stochastic fractional heroin model with artificial decay term

Heroin addiction is a continuously progressing phenomenon that represents a major problem for world's the public health; this indicates that the development of new methodologies to address the issue at the international level is a crucial priority. To study its transmission dynamics, a new stoc...

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Main Authors: Feliz Minhós, Ali Raza, Umar Shafique
Format: Article
Language:English
Published: AIMS Press 2025-03-01
Series:AIMS Mathematics
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Online Access:https://www.aimspress.com/article/doi/10.3934/math.2025278
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author Feliz Minhós
Ali Raza
Umar Shafique
author_facet Feliz Minhós
Ali Raza
Umar Shafique
author_sort Feliz Minhós
collection DOAJ
description Heroin addiction is a continuously progressing phenomenon that represents a major problem for world's the public health; this indicates that the development of new methodologies to address the issue at the international level is a crucial priority. To study its transmission dynamics, a new stochastic fractional delayed heroin model based on stochastic fractional delay differential equations (SFDDEs) was developed to focus on the positive aspects of randomness and memory effects. The positive, boundedness, existence, and uniqueness of the model were studied rigorously. The equilibria (i.e., heroin-free equilibrium and the present equilibrium, which gives a clue about both eradication and persistence cases), reproduction number, and sensitivity of parameters were analyzed. The local and global stability of the new model was studied around its steady states. Also, well-known theorems are presented to investigate the extinction and persistence of heroin. The Grunwald-Letnikove non-standard finite difference (GL-NSFD) method was used for the efficient computational analysis of the stochastic fractional delayed model. For the dynamical consistency of the model, the positivity and boundedness of an efficient method were studied rigorously. The given study focuses on delay strategies and fractional calculus that could be useful in formulating specific measures for regulating addiction. Moreover, the simulated results support the theoretical analysis of the model and validate it.
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spelling doaj-art-be75d20d51fc4f528b624dbcec16e7a22025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-03-011036102612710.3934/math.2025278An efficient computational analysis for stochastic fractional heroin model with artificial decay termFeliz Minhós0Ali Raza1https://orcid.org/0000-0002-6443-9966Umar Shafique2https://orcid.org/0009-0007-6472-8040Department of Mathematics, School of Science and Technology, University of Évora, Rua Romão Ramalho, 59, Évora, 7000-671, PortugalCenter for Research in Mathematics and Applications (CIMA), Institute for Advanced Studies and Research (IIFA), University of Évora, Rua Romão Ramalho, 59, Évora, 7000-671, PortugalDepartment of Mathematics, National College of Business Administration and Economics, Lahore, 54660, PakistanHeroin addiction is a continuously progressing phenomenon that represents a major problem for world's the public health; this indicates that the development of new methodologies to address the issue at the international level is a crucial priority. To study its transmission dynamics, a new stochastic fractional delayed heroin model based on stochastic fractional delay differential equations (SFDDEs) was developed to focus on the positive aspects of randomness and memory effects. The positive, boundedness, existence, and uniqueness of the model were studied rigorously. The equilibria (i.e., heroin-free equilibrium and the present equilibrium, which gives a clue about both eradication and persistence cases), reproduction number, and sensitivity of parameters were analyzed. The local and global stability of the new model was studied around its steady states. Also, well-known theorems are presented to investigate the extinction and persistence of heroin. The Grunwald-Letnikove non-standard finite difference (GL-NSFD) method was used for the efficient computational analysis of the stochastic fractional delayed model. For the dynamical consistency of the model, the positivity and boundedness of an efficient method were studied rigorously. The given study focuses on delay strategies and fractional calculus that could be useful in formulating specific measures for regulating addiction. Moreover, the simulated results support the theoretical analysis of the model and validate it.https://www.aimspress.com/article/doi/10.3934/math.2025278heroin modelstochastic fractional delay differential equations (sfddes)existence and uniquenessstability resultsextinction and persistencegl-nsfdresults
spellingShingle Feliz Minhós
Ali Raza
Umar Shafique
An efficient computational analysis for stochastic fractional heroin model with artificial decay term
AIMS Mathematics
heroin model
stochastic fractional delay differential equations (sfddes)
existence and uniqueness
stability results
extinction and persistence
gl-nsfd
results
title An efficient computational analysis for stochastic fractional heroin model with artificial decay term
title_full An efficient computational analysis for stochastic fractional heroin model with artificial decay term
title_fullStr An efficient computational analysis for stochastic fractional heroin model with artificial decay term
title_full_unstemmed An efficient computational analysis for stochastic fractional heroin model with artificial decay term
title_short An efficient computational analysis for stochastic fractional heroin model with artificial decay term
title_sort efficient computational analysis for stochastic fractional heroin model with artificial decay term
topic heroin model
stochastic fractional delay differential equations (sfddes)
existence and uniqueness
stability results
extinction and persistence
gl-nsfd
results
url https://www.aimspress.com/article/doi/10.3934/math.2025278
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