Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor

Agustianingsih, Susi; Reorita, Rina; Renny, Renny

doi:10.20956/jmsk.v16i3.6942

Journal

Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor

Jurnal Matematika, Statistika dan Komputasi · Vol. 16 No. 3 (2020) · pp. 311–324

DOI: 10.20956/jmsk.v16i3.6942
ISSN: 2614-8811, 1858-1382
Published: 2020-04-28
Publisher: Department of Mathematics, Hasanuddin University
Language: en

Abstract

The SIR model is one of the mathematical model which describes the characteristic of the spread of infectious disease in differential equation form by dividing the human populations into three groups. There are individual susceptible group, individual infective group, and individual recovered group. This model involves vaccination, quarantine, and immigration factors. Vaccination and quarantine must be given as much as it needs, so a control is required to minimize infection of disease and the number of individual infective with a minimum costs. In this research, optimal control of SIR model with vaccination, quarantine, and immigration factor is solved by using Pontryagin maximum principle and numerically simulated by using Runge-Kutta method. Numerical simulation results show optimal control of treatment, citizen of vaccination, immigrant of vaccination, and quarantine will accelerate the decline of infected number with the minimum cost, compared with the optimal control of SIR model without quarantine factor.

Keywords

Collaboration network of the authors

10 authors · 13 co-authorship links

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Gunadarma University
Affiliation unknown

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Co-author	Organisation	Joint articles
Joko Purwanto	Gunadarma University	1
Mashuri Mashuri	Affiliation unknown	1
Yayah Zakiyah	Affiliation unknown	1
Agus Yodi Gunawan	Affiliation unknown	1
Novry Erwina	Affiliation unknown	1
Sri Maryani	Affiliation unknown	1
Amalina Zahrina	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">Optimal control for SIR Model with The Influence of Vaccination, Quarantine and Immigration factor</dc:title>
	<dc:creator xml:lang="en">Agustianingsih, Susi</dc:creator>
	<dc:creator xml:lang="en">Reorita, Rina</dc:creator>
	<dc:creator xml:lang="en">Renny, Renny</dc:creator>
	<dc:subject xml:lang="en">Quarantine</dc:subject>
	<dc:subject xml:lang="en">optimal control</dc:subject>
	<dc:subject xml:lang="en">SIR model</dc:subject>
	<dc:subject xml:lang="en">Pontryagin maximum principle</dc:subject>
	<dc:subject xml:lang="en">vaccination</dc:subject>
	<dc:description xml:lang="en">The SIR model is one of the mathematical model which describes the characteristic of the spread of infectious disease in differential equation form by dividing the human populations into three groups. There are individual susceptible group, individual infective group, and individual recovered group. This model involves vaccination, quarantine, and immigration factors. Vaccination and quarantine must be given as much as it needs, so a control is required to minimize infection of disease and the number of individual infective with a minimum costs. In this research, optimal control of SIR model with vaccination, quarantine, and immigration factor is solved by using Pontryagin maximum principle and numerically simulated by using Runge-Kutta method. Numerical simulation results show optimal control of treatment, citizen of vaccination, immigrant of vaccination, and quarantine will accelerate the decline of infected number with the minimum cost, compared with the optimal control of SIR model without quarantine factor.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2020-04-28</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
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	<dc:identifier>10.20956/jmsk.v16i3.6942</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 16 No. 3 (2020): JMSK, MAY, 2020; 311-324</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/6942/pdf</dc:relation>
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	<dc:rights xml:lang="en">Copyright (c) 2020 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
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