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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.

Bahasa Indonesia

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

38 authors · 96 co-authorship links

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Co-authorOrganisationJoint articles
Syamsuddin ToahaAffiliation unknown4
Suriani MAffiliation unknown3
I Nyoman WidanaAffiliation unknown2
Hartina HusainAffiliation unknown2
Kasbawati KasbawatiAffiliation unknown2
La Ode Muh UmranAffiliation unknown1
Sukriyanti SukriyantiAffiliation unknown1
Nurnia NurniaAffiliation unknown1
Hilaluddin HanafiAffiliation unknown1
Fitra SalehAffiliation unknown1
Djafar MeyAffiliation unknown1
Asnani AsnaniAffiliation unknown1
Kobajashi Togo IsamuAffiliation unknown1
Meysa Atika PuteriAffiliation unknown1
Threevaldo Joan SaputraAffiliation unknown1
Musdalifah Akbar SimanjuntakAffiliation unknown1
Edwin RandalangiAffiliation unknown1
Athira SalsabilaAffiliation unknown1
Andi Hamril Vikri Al FarisiAffiliation unknown1
Ita FitriaAffiliation unknown1
Ni Luh Putu SuciptawatiAffiliation unknown1
kusnaeni kusnaeniAffiliation unknown1
Nur RahmiAffiliation unknown1
Muhammad Arkam ArifuddinAffiliation unknown1
Jeffry KusumaAffiliation unknown1
Wahyuni EkasasmitaAffiliation unknown1
Restu Ananda PutraAffiliation unknown1
Sri Muslihah BakhtiarAffiliation unknown1
Ratmawati MalakaAffiliation unknown1
Dwi MaryanaAffiliation unknown1
Fatma MaruddinAffiliation unknown1
Ali Akbar WahabAffiliation 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 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>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/23989</dc:identifier>
	<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>
	<dc:relation>10.20956/j.v19i2.23989.g9160</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2023 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
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