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FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 1 (2025) · pp. 511–524

DOI
10.30598/barekengvol19iss1pp511-524
ISSN
2615-3017, 1978-7227
Published
2025-01-13
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

Drug abuse poses significant challenges to public health and socio-economic stability worldwide. Narcotics, which are psychotropic compounds, are typically used for treating specific medical conditions. Currently, many individuals abuse drugs outside of the function of treatment. This misuse leads to central nervous system disorders, resulting in significant mental and behavioral health issues. In this article, we discuss a fractional-order mathematical model for the transmission of drug users with fractional-order α∈ (0,1]. We employ fractional-order differential equations using the Caputo derivative approach to model the transmission dynamics. We analyze the local stability of drug-free and endemic equilibrium points and calculate the basic reproduction number (). Our analysis indicates that the drug-free equilibrium is locally asymptotically stable when, while the endemic equilibrium is stable when. We implement a numerical scheme to simulate the fractional-order model, illustrating the theoretical findings.

Collaboration network of the authors

32 authors · 75 co-authorship links · 28 across different organisations

Hover or tap a name to highlight its co-authors. Double-click to open the author's page.

  • Universitas Airlangga
  • Hasanuddin University
  • Universitas Halu Oleo
  • Universitas Islam Negeri Palopo
  • Universitas Gadjah Mada
  • Diponegoro University
  • Federal University of Technology
  • Other organisations
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Fatmawati - FatmawatiAffiliation unknown3
Muhammad Abdurrahman RoisAffiliation unknown2
Ananda NoersenaUniversitas Airlangga2
Afeez AbidemiFederal University of Technology2
Nabil Azizul HakimUniversitas Airlangga2
Faishal Farrel HerdichoUniversitas Airlangga2
John Olajide AkanniKolaDaisi University2
Wahyuni HusainUniversitas Islam Negeri Palopo1
Muhammad Ashabul KahfiUniversitas Islam Negeri Palopo1
Agus IndiyantoUniversitas Gadjah Mada1
Bahtiar BahtiarUniversitas Halu Oleo1
Fitriah AmirUniversitas Halu Oleo1
Stefanie Jessica Henny LarasatiDiponegoro University1
Chairun Annisa AryantiUniversitas Halu Oleo1
Retno FitriantiHasanuddin University1
Insany Fitri NurqamarHasanuddin University1
Mirzalina ZaenalHasanuddin University1
Daniella Cynthia SHasanuddin University1
Wahda WahdaHasanuddin University1
Ahmadin AhmadinUniversitas Airlangga1
Abyan Daffa AkbarUniversitas Airlangga1
Mohamad IsramAffiliation unknown1
Sara Wibawaning RespatiPoliteknik Negeri Balikpapan1
Sri KusriniAffiliation unknown1
Anisa PuspitasariAffiliation unknown1
Miswanto MiswantoAffiliation unknown1
Erzalina Ayu Satya MeganandaAffiliation unknown1
Muhammad FarmanAffiliation unknown1
Khadija JamilAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">FRACTIONAL-ORDER MODEL OF THE DRUG USER TRANSMISSION</dc:title>
	<dc:creator>Izzati, Indah Nurun</dc:creator>
	<dc:creator>Fatmawati, Fatmawati</dc:creator>
	<dc:creator>Alfiniyah, Cicik</dc:creator>
	<dc:description xml:lang="en-US">Drug abuse poses significant challenges to public health and socio-economic stability worldwide. Narcotics, which are psychotropic compounds, are typically used for treating specific medical conditions. Currently, many individuals abuse drugs outside of the function of treatment. This misuse leads to central nervous system disorders, resulting in significant mental and behavioral health issues. In this article, we discuss a fractional-order mathematical model for the transmission of drug users with fractional-order α∈ (0,1]. We employ fractional-order differential equations using the Caputo derivative approach to model the transmission dynamics. We analyze the local stability of drug-free and endemic equilibrium points and calculate the basic reproduction number (). Our analysis indicates that the drug-free equilibrium is locally asymptotically stable when , while the endemic equilibrium is stable when . We implement a numerical scheme to simulate the fractional-order model, illustrating the theoretical findings.
&amp;nbsp;</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-01-13</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14594</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss1pp511-524</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application; 511-524</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss1year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/14594/9567</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Indah Nurun Izzati, Fatmawati Fatmawati, Cicik Alfiniyah</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
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