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Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse

Jurnal Matematika, Statistika dan Komputasi · Vol. 17 No. 3 (2021) · pp. 339–348

DOI
10.20956/j.v17i3.12467
ISSN
2614-8811, 1858-1382
Published
2021-05-12
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.

Bahasa Indonesia

Abstrak Artikel ini membahas tentang kontrol optimal model matematika dinamika penyebaran penyalahgunaan narkoba. Model ini terdiri dari lima kelas populasi, yaitu rentan menggunakan narkoba atau Susceptible (S), penyalahgunaan narkoba tingkat ringan atau Lighter Users (A), penyalahgunaan narkoba tingkat berat atau Heavy Users (H), penyalahgunaan narkoba melakukan pengobatan atau Treatment (T), dan penyalahgunaan narkoba sembuh dan mengalami pemulihan atau Recovery (R). Sistem diselesaikan dengan menggunakan prinsip minimum Pontryagin dan secara numerik dengan metode forward-backward sweep. Simulasi numerik dari masalah optimal menunjukkan bahwa dengan adanya upaya penerapan kampanye anti narkoba dan penguatan terhadap psikologi diri lewat konseling maka penyebaran penyalahgunaan narkoba dapat lebih cepat diberantas. Penerapan kampanye dan penguatan terhadap psikologi diri lewat konseling dalam jumlah besar perlu dilakukan sejak awal kemudian proporsinya dapat dikurangi sampai waktu tertentu tidak perlu lagi diberikan. Penggunaan kontrol berupa upaya penguatan terhadap psikologi diri lewat konseling lebih besar artinya perlu dilakukan dalam waktu yang lebih lama untuk mencegah terjadinya penyebaran penyalahgunaan narkoba.

Keywords

Collaboration network of the authors

31 authors · 61 co-authorship links

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

  • State University of Makassar
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Khaeruddin KhaeruddinState University of Makassar3
Sulma SulmaAffiliation unknown3
Jeffry KusumaAffiliation unknown2
Syamsul AgusAffiliation unknown2
Yusrianto YusriantoAffiliation unknown2
Himmatul Ulya FebriyantiAffiliation unknown2
Lilis Dwi Sapta AprilyaniAffiliation unknown2
Suriani SurianiAffiliation unknown2
Syamsir MuarafAffiliation unknown2
Andi Utari SamsirAffiliation unknown2
Mutmainnah SyamsulAffiliation unknown2
Rabiatul AdawiyahAffiliation unknown2
I Nyoman WidanaAffiliation unknown1
Ita FitriaAffiliation unknown1
Sulfayanti SulfayantiAffiliation unknown1
Mawardi BahriAffiliation unknown1
IIN SUTRISNAAffiliation unknown1
Asriadi NasrunAffiliation unknown1
A. Muh. Amil SiddikAffiliation unknown1
Andi Muhammad AnwarAffiliation unknown1
Nur Suci RamadhaniAffiliation unknown1
Toaha ToahaAffiliation unknown1
Hukmah HukmahAffiliation unknown1
Ismi Ra'yan SyarifAffiliation unknown1
Sitti SahrimanAffiliation unknown1
Anisa KalondengAffiliation unknown1
M. Zaky Hisyam GozhiAffiliation unknown1
Aidul Fitri MustaminAffiliation 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://journal.unhas.ac.id/index.php/jmsk/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Optimal Control of Mathematical Models on The Dynamics Spread of Drug Abuse</dc:title>
	<dc:creator xml:lang="en">Anggriani, Nita</dc:creator>
	<dc:creator xml:lang="en">Toaha, Syamsuddin </dc:creator>
	<dc:creator xml:lang="en">Kasbawati, Kasbawati</dc:creator>
	<dc:subject xml:lang="en">The Dynamics of Drug Abuse Spread</dc:subject>
	<dc:subject xml:lang="en">Mathematical Model</dc:subject>
	<dc:subject xml:lang="en">Pontryagin Minimum Principles</dc:subject>
	<dc:subject xml:lang="en">Forward-Backward Sweep Method</dc:subject>
	<dc:subject xml:lang="en">Optimal Control</dc:subject>
	<dc:description xml:lang="en">This article examines the optimal control of a mathematical model of the spread of drug abuse. This model consists of five population classes, namely susceptible to using drugs (S), light-grade drugs (A), heavy-grade drugs (H), medicated drugs (T), and Recovery from drugs (R). The system is solved using the Pontryagin minimum principle and numerically by the forward-backward sweep method. Numerical simulations of the optimal problem show that with the implementation of anti-drug campaigns and strengthening of self-psychology through counseling, the spread of drug abuse can be eradicated more quickly. The implementation of campaigns and strengthening of self-psychology through large amounts of counseling needs to be done from the beginning then the proportion can be reduced until a certain time does not need to be given anymore. The use of control in the form of strengthening efforts to self-psychology through counseling means that it needs to be done in a longer time to prevent the spread of drug abuse.</dc:description>
	<dc:description xml:lang="id">Abstrak 
Artikel ini membahas tentang kontrol optimal model matematika dinamika penyebaran penyalahgunaan narkoba. Model ini terdiri dari lima kelas populasi, yaitu rentan menggunakan narkoba atau Susceptible (S), penyalahgunaan narkoba tingkat ringan atau Lighter Users (A), penyalahgunaan narkoba &amp;nbsp;tingkat berat atau Heavy Users (H), penyalahgunaan narkoba melakukan pengobatan atau Treatment (T), dan penyalahgunaan narkoba sembuh dan mengalami pemulihan atau Recovery (R). Sistem diselesaikan dengan menggunakan prinsip minimum Pontryagin dan secara numerik dengan metode forward-backward sweep. Simulasi numerik dari masalah optimal menunjukkan bahwa dengan adanya upaya penerapan kampanye anti narkoba dan penguatan terhadap psikologi diri lewat konseling maka penyebaran penyalahgunaan narkoba dapat lebih cepat diberantas. Penerapan kampanye dan penguatan terhadap psikologi diri lewat konseling dalam jumlah besar perlu dilakukan sejak awal kemudian proporsinya dapat dikurangi sampai waktu tertentu tidak perlu lagi diberikan. Penggunaan kontrol berupa upaya penguatan terhadap psikologi diri lewat konseling lebih besar artinya perlu dilakukan dalam waktu yang lebih lama untuk mencegah terjadinya penyebaran penyalahgunaan narkoba.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2021-05-12</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://journal.unhas.ac.id/index.php/jmsk/article/view/12467</dc:identifier>
	<dc:identifier>10.20956/j.v17i3.12467</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 17 No. 3 (2021):  May, 2021; 339-348</dc:source>
	<dc:source>2614-8811</dc:source>
	<dc:source>1858-1382</dc:source>
	<dc:language>en</dc:language>
	<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/12467/6704</dc:relation>
	<dc:relation>10.20956/j.v17i3.12467.g6704</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2021 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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