Mathematical Model of COVID-19 with Quarantine and Vaccination

HUkmah, Hukmah; Nisardi, Muhammad Rifki; Sulma, Sulma; M, Suriani

doi:10.20956/j.v19i2.22301

Open access Jurnal

Mathematical Model of COVID-19 with Quarantine and Vaccination

Model Matematika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi

Jurnal Matematika, Statistika dan Komputasi · Vol. 19 No. 2 (2023) · pp. 266–285

DOI: 10.20956/j.v19i2.22301
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

Abstract We present a mathematical model of COVID-19 disease by modifying the SEIR model. The model considers two additional compartments, quarantine (Q) and vaccination (V) which aim to control the spread of COVID-19. Based on the model, we obtained a disease-free equilibrium point and an endemic equilibrium point. The basic reproduction numbers were calculated using the next-generation matrix method. In this model, we analyzed the stability conditions that must be satisfied by the defining parameters. We perform data on the spread of COVID-19 in Indonesia for estimation to provide the parameter value in the model. Based on the result, there is an influence of changes in several parameter values on the number of individuals infected with COVID-19.

Bahasa Indonesia

Abstrak Dalam penelitian ini, diberikan model matematika penyebaran penyakit COVID-19 dengan memodifikasi model SEIR. Model yang digunakan mempertimbangkan dua kompartemen tambahan yaitu karantina (Q) dan vaksinasi (V) sebagai usaha untuk mengendalikan penyebaran COVID-19. Berdasarkan model yang telah dibangun, diperoleh titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Nilai bilangan reproduksi dasar dihitung dengan menggunakan metode matriks next generation. Dalam model ini juga diperoleh syarat kestabilan yang harus dipenuhi oleh parameter yang telah didefinisikan. Data penyebaran COVID-19 di Indonesia digunakan untuk memberikan estimasi nilai parameter pada model. Berdasarkan analisa yang diperoleh, terdapat pengaruh dari perubahan beberapa nilai parameter terhadap jumlah individu terinfeksi COVID-19.

Keywords

Collaboration network of the authors

20 authors · 53 co-authorship links

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Co-author	Organisation	Joint articles
Syamsuddin Toaha	Affiliation unknown	3
Suriani Suriani	Affiliation unknown	3
Harianto Harianto	Affiliation unknown	3
Dian Firmayasari	Affiliation unknown	3
I Nyoman Widana	Affiliation unknown	2
Hartina Husain	Affiliation unknown	2
Ita Fitria	Affiliation unknown	1
Ni Luh Putu Suciptawati	Affiliation unknown	1
kusnaeni kusnaeni	Affiliation unknown	1
Nur Rahmi	Affiliation unknown	1
Muhammad Arkam Arifuddin	Affiliation unknown	1
Kasbawati Kasbawati	Affiliation unknown	1
Jeffry Kusuma	Affiliation unknown	1
Wahyuni Ekasasmita	Affiliation unknown	1
Restu Ananda Putra	Affiliation unknown	1
Sri Muslihah Bakhtiar	Affiliation unknown	1

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">Mathematical Model of COVID-19 with Quarantine and Vaccination</dc:title>
	<dc:title xml:lang="id">Model Matematika Penyebaran Covid-19 Dengan Karantina Dan Vaksinasi </dc:title>
	<dc:creator xml:lang="en">HUkmah, Hukmah</dc:creator>
	<dc:creator xml:lang="en">Nisardi, Muhammad Rifki </dc:creator>
	<dc:creator xml:lang="en">Sulma, Sulma</dc:creator>
	<dc:creator xml:lang="en">M, Suriani </dc:creator>
	<dc:subject xml:lang="en">SEIR-VQ Model</dc:subject>
	<dc:subject xml:lang="en">Basic Reproduction Numbers</dc:subject>
	<dc:subject xml:lang="en">Next Generation Matrix</dc:subject>
	<dc:description xml:lang="en">Abstract 
We present a mathematical model of COVID-19 disease by modifying the SEIR model. The model considers two additional compartments, quarantine (Q) and vaccination (V) which aim to control the spread of COVID-19. Based on the model, we obtained a disease-free equilibrium point and an endemic equilibrium point. The basic reproduction numbers were calculated using the next-generation matrix method. In this model, we analyzed the stability conditions that must be satisfied by the defining parameters. We perform data on the spread of COVID-19 in Indonesia for estimation to provide the parameter value in the model. Based on the result, there is an influence of changes in several parameter values on the number of individuals infected with COVID-19.
 </dc:description>
	<dc:description xml:lang="id">Abstrak 
Dalam penelitian ini, diberikan model matematika penyebaran penyakit COVID-19 dengan memodifikasi model SEIR. Model yang digunakan mempertimbangkan dua kompartemen tambahan yaitu karantina (Q) dan vaksinasi (V) sebagai usaha untuk mengendalikan penyebaran COVID-19. Berdasarkan model yang telah dibangun, diperoleh titik kesetimbangan bebas penyakit dan titik kesetimbangan endemik. Nilai bilangan reproduksi dasar &amp;nbsp;dihitung dengan menggunakan metode matriks next generation. Dalam model ini juga diperoleh syarat kestabilan yang harus dipenuhi oleh parameter yang telah didefinisikan. Data penyebaran COVID-19 di Indonesia digunakan untuk memberikan estimasi nilai parameter pada model. Berdasarkan analisa yang diperoleh, terdapat pengaruh dari perubahan beberapa nilai parameter terhadap jumlah individu terinfeksi COVID-19.
&amp;nbsp;
&amp;nbsp;</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>
	<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/22301</dc:identifier>
	<dc:identifier>10.20956/j.v19i2.22301</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 19 No. 2 (2023): JANUARY 2023; 266-285</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/22301/9146</dc:relation>
	<dc:relation>10.20956/j.v19i2.22301.g9146</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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