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Optimal Control of the Dynamics of the Spread of Covid-19 With Quarantine and Vaccination: Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi

Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi: Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 2 (2023) · pp. 374–390

DOI
10.20956/j.v19i2.23989
ISSN
2614-8811, 1858-1382
Published
2023-01-05
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

English

Vaccination and quarantine are effective ways to control the spread of disease. Vaccination helps susceptible individuals to boost immunity. Additionally, quarantine helps reduce interactions which will reduce the infection rate. This study proposed the SEIR mathematical model to describe the dynamics of the spread of COVID-19 by providing control in the form of vaccination and quarantine. Based on Pontryagin's minimum principle, the optimal system for optimal control problems is derived and solved numerically using the Fourth Order Runge-Kutta scheme with the Forward-Backward Sweep approach. A numerical simulation of the optimal problem showed that the spread of disease is eradicated more quickly by vaccination and quarantine. Vaccination in large numbers is needed earlier if the rate of contact transmission is high enough. The provision of quarantine control is required from the beginning until no longer to be applied. A large proportion of quarantine at the beginning of time can suppress the spread of disease in the population.

Indonesian

Vaksinasi dan Karantina merupakan cara yang efektif untuk mengendalikan penyebaran penyakit. Vaksinasi membantu individu yang rentan untuk meningkatkan kekebalan tubuh dan karantina membantu mengurangi interaksi sehingga laju penyebaran penyakit dapat berkurang. Dalam penelitian ini diberikan model matematika SEIR untuk menggambarkan dinamika penyebaran COVID-19 dengan memberikan kontrol berupa vaksinasi dan karantina. Berdasarkan prinsip minimum Pontryagin sistem optimalitas untuk masalah kontrol optimal diturunkan dan diselesaikan secara numerik menggunakan skema Runge-Kutta Orde Empat dengan pendekatan Forward-Backward Sweep. Simulasi numerik dari masalah optimal menunjukkan bahwa dengan pemberian vaksinasi dan karantina maka penyebaran penyakit lebih cepat diberantas. Vaksinasi dalam jumlah besar perlu dilakukan sejak awal jika laju transmisi kontak cukup tinggi. Pemberian kontrol karantina dalam jumlah besar perlu dilakukan sejak awal kemudian proporsinya dikurangi sampai waktu tertentu tidak perlu lagi diberikan. Dengan pemberian proporsi karantina yang besar di awal waktu mampu menekan terjadinya penyebaran penyakit dalam populasi.

Keywords

Collaboration network of the authors

40 authors · 154 co-authorship links · 22 across different organisations · showing the 40 most connected

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

  • Hasanuddin University
  • Institut Teknologi Bacharuddin Jusuf Habibie
  • Universitas Muhammadiyah Bulukumba
  • Udayana University
  • Universitas Gadjah Mada
  • Universitas Muhammadiyah Kolaka Utara
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Syamsuddin ToahaHasanuddin University3
M SurianiUniversitas Muhammadiyah Bulukumba3
I NYOMAN WIDANAUdayana University2
Hartina HusainInstitut Teknologi Bacharuddin Jusuf Habibie2
Kasbawati KasbawatiHasanuddin University2
Meysa Atika PuteriAffiliation unknown1
Threevaldo Joan SaputraAffiliation unknown1
Musdalifah Akbar SimanjuntakAffiliation unknown1
Edwin RandalangiAffiliation unknown1
Athira SalsabilaAffiliation unknown1
Andi Hamril Vikri Al FarisiAffiliation unknown1
Meysa Atika PuteriHasanuddin University1
Harianto HariantoHasanuddin University1
Threevaldo Joan SaputraHasanuddin University1
Musdalifah Akbar SimanjuntakHasanuddin University1
Edwin RandalangiHasanuddin University1
Athira SalsabilaHasanuddin University1
Andi Hamril Vikri Al FarisiHasanuddin University1
Harianto HariantoHasanuddin University1
Ita FitriaUniversitas Muhammadiyah Bulukumba1
NI LUH PUTU SUCIPTAWATIUdayana University1
Nur RahmiInstitut Teknologi Bacharuddin Jusuf Habibie1
Muhammad Arkam ArifuddinInstitut Teknologi Bacharuddin Jusuf Habibie1
Kusnaeni KusnaeniInstitut Teknologi Bacharuddin Jusuf Habibie1
Restu Ananda PutraUniversitas Gadjah Mada1
Sri Muslihah BakhtiarUniversitas Muhammadiyah Kolaka Utara1
Wahyuni EkasasmitaInstitut Teknologi Bacharuddin Jusuf Habibie1
Juhadi JuhadiAffiliation unknown1
Sula Ari ApriantoAffiliation unknown1
Ananto AjiAffiliation unknown1
Rakhman SofyanAffiliation unknown1
Siti JahrohAffiliation unknown1
Rike SitioAffiliation unknown1
Suprehatin SuprehatinAffiliation 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 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">Optimal Control of the Dynamics of the Spread of Covid-19 With Quarantine and Vaccination : Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi</dc:title>
	<dc:title xml:lang="id">Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi: Kontrol Optimal Dinamika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi</dc:title>
	<dc:creator xml:lang="en">Sulma, Sulma</dc:creator>
	<dc:creator xml:lang="en">Nisardi, Muhammad Rifki </dc:creator>
	<dc:creator xml:lang="en">Suriani, Suriani</dc:creator>
	<dc:creator xml:lang="en">Hukmah, Hukmah</dc:creator>
	<dc:creator xml:lang="en">Harianto, Harianto</dc:creator>
	<dc:creator xml:lang="en">Firmayasari, Dian </dc:creator>
	<dc:subject xml:lang="en">Selected:SEIR Model</dc:subject>
	<dc:subject xml:lang="en">Minimum Pontryagin Principle</dc:subject>
	<dc:subject xml:lang="en">Fourth Runge-Kutta</dc:subject>
	<dc:description xml:lang="en">Vaccination and quarantine are effective ways to control the spread of disease. Vaccination helps susceptible individuals to boost immunity. Additionally, quarantine helps reduce interactions which will reduce the infection rate. This study proposed the SEIR mathematical model to describe the dynamics of the spread of COVID-19 by providing control in the form of vaccination and quarantine. Based on Pontryagin's minimum principle, the optimal system for optimal control problems is derived and solved numerically using the Fourth Order Runge-Kutta scheme with the Forward-Backward Sweep approach. A numerical simulation of the optimal problem showed that the spread of disease is eradicated more quickly by vaccination and quarantine. Vaccination in large numbers is needed earlier if the rate of contact transmission is high enough. The provision of quarantine control is required from the beginning until no longer to be applied. A large proportion of quarantine at the beginning of time can suppress the spread of disease in the population.
 </dc:description>
	<dc:description xml:lang="id">Vaksinasi dan Karantina merupakan cara yang efektif untuk mengendalikan penyebaran penyakit. Vaksinasi membantu individu yang rentan untuk meningkatkan kekebalan tubuh dan karantina membantu mengurangi interaksi sehingga laju penyebaran penyakit dapat berkurang. Dalam penelitian ini diberikan model matematika SEIR untuk menggambarkan dinamika penyebaran COVID-19 dengan memberikan kontrol berupa vaksinasi dan karantina. Berdasarkan prinsip minimum Pontryagin sistem optimalitas untuk masalah kontrol optimal diturunkan dan diselesaikan secara numerik menggunakan skema Runge-Kutta Orde Empat dengan pendekatan Forward-Backward Sweep. Simulasi numerik dari masalah optimal menunjukkan bahwa dengan pemberian vaksinasi dan karantina maka penyebaran penyakit lebih cepat diberantas. Vaksinasi dalam jumlah besar perlu dilakukan sejak awal jika laju transmisi kontak cukup tinggi. Pemberian kontrol karantina dalam jumlah besar perlu dilakukan sejak awal kemudian proporsinya dikurangi sampai waktu tertentu tidak perlu lagi diberikan. Dengan pemberian proporsi karantina yang besar di awal waktu mampu menekan terjadinya penyebaran penyakit dalam populasi.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2023-01-05</dc:date>
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	<dc:identifier>10.20956/j.v19i2.23989</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 2 (2023): JANUARY 2023; 374-390</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/23989/9160</dc:relation>
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	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
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