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Optimal Control of a Mathematical Model of Smoking with Temporary Quitters and Permanent Quitters

Kontrol Optimal Model Matematika Merokok dengan Perokok Berhenti Sementara dan Perokok Berhenti Permanen

Jurnal Matematika, Statistika dan Komputasi · Vol. 18 No. 1 (2021) · pp. 42–54

DOI
10.20956/j.v18i1.13974
ISSN
2614-8811, 1858-1382
Published
2021-09-02
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Abstract This article discusses the optimal control of a mathematical model on smoking. This model consists of six population classes, namely potential to become smoker snuffing class irregular smokers regular smokers temporary quitters and permanent quitters The completion of this research uses the Pontryagin minimum principle and numerically using the forward-backward Sweep method. Numerical simulations of the optimal problem show that with the implementation of education campaigns and anti-nicotine medicine, the smokers can be decreased more quickly and the smoking population who quit permanently can be increased. The implementation of both through large amounts needs to be done from the beginning. The use of control in the form of education campaigns is of great value until the end of the research period means that it needs to be done continuously to reduce the number of smokers in the population.

Bahasa Indonesia

Abstrak Artikel ini membahas tentang kontrol optimal model matematika merokok. Model ini terdiri dari enam kelas populasi, yaitu berpotensi sebagai perokok atau Potential Smokers (P), Snuffing Class (S), perokok tidak aktif atau Irregular Smokers (X), perokok aktif atau Regular Smokers (Y), perokok yang berhenti sementara atau Temporary Quitters (Qt) dan perokok yang berhenti permanen atau Permanent Quitters (Qp). Sistem diselesaikan dengan menggunakan prinsip minimum Pontryagin dan secara numerik diselesaikan dengan metode forward-backward Sweep. Simulasi numerik dari masalah optimal menunjukkan bahwa dengan adanya penerapan kampanye edukasi dan pemberian obat anti nikotin maka perilaku merokok lebih cepat berkurang dan meningkatkan populasi perokok yang berhenti secara permanen. Penerapan kedua kontrol tersebut dalam jumlah besar perlu dilakukan sejak awal. Penggunaan kontrol berupa kampanye edukasi bernilai besar hingga akhir tahun pengamatan artinya untuk menekan jumlah populasi perokok secara maksimal, kampanye edukasi harus dilakukan secara terus menerus.

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
Nita AnggrianiAffiliation 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 a Mathematical Model of Smoking with Temporary Quitters and Permanent Quitters</dc:title>
	<dc:title xml:lang="id">Kontrol Optimal Model Matematika Merokok dengan Perokok Berhenti Sementara dan Perokok Berhenti Permanen</dc:title>
	<dc:creator xml:lang="en">Samsir, Andi Utari</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">Mathematical Model on Smoking</dc:subject>
	<dc:subject xml:lang="en">ontryagin Minimum Principle</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">Abstract
This article discusses the optimal control of a mathematical model on smoking. This model consists of six population classes, namely potential to become smoker  snuffing class  irregular smokers regular smokers  temporary quitters  and permanent quitters  The completion of this research uses the Pontryagin minimum principle and numerically using the forward-backward Sweep method. Numerical simulations of the optimal problem show that with the implementation of education campaigns and anti-nicotine medicine, the smokers can be decreased more quickly and the smoking population who quit permanently can be increased. The implementation of both through large amounts needs to be done from the beginning. The use of control in the form of education campaigns is of great value until the end of the research period means that it needs to be done continuously to reduce the number of smokers in the population.
 </dc:description>
	<dc:description xml:lang="id">Abstrak
Artikel ini membahas tentang kontrol optimal model matematika merokok. Model ini terdiri dari enam kelas populasi, yaitu berpotensi sebagai perokok atau Potential Smokers (P), Snuffing Class (S), perokok tidak aktif atau Irregular Smokers (X), perokok aktif atau Regular Smokers (Y),&amp;nbsp;perokok yang berhenti sementara atau Temporary Quitters (Qt)&amp;nbsp;dan perokok yang berhenti permanen atau Permanent Quitters (Qp). Sistem diselesaikan dengan menggunakan prinsip minimum Pontryagin dan secara numerik diselesaikan dengan metode forward-backward Sweep. Simulasi numerik dari masalah optimal menunjukkan bahwa dengan adanya penerapan kampanye edukasi dan pemberian obat anti nikotin maka perilaku merokok lebih cepat berkurang dan meningkatkan populasi perokok yang berhenti secara permanen. Penerapan kedua kontrol tersebut dalam jumlah besar perlu dilakukan sejak awal. Penggunaan kontrol berupa kampanye edukasi bernilai besar hingga akhir tahun pengamatan artinya untuk menekan jumlah populasi perokok secara maksimal, kampanye edukasi harus dilakukan secara terus menerus.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2021-09-02</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/13974</dc:identifier>
	<dc:identifier>10.20956/j.v18i1.13974</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 18 No. 1 (2021): September 2021; 42-54</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/13974/7294</dc:relation>
	<dc:relation>10.20956/j.v18i1.13974.g7294</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>
</oai_dc:dc>