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

Jurnal

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

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

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

Abstrak

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.

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Gunadarma University
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Rekan penulis	Organisasi	Artikel bersama
Joko Purwanto	Gunadarma University	1
Mashuri Mashuri	Afiliasi tidak diketahui	1
Yayah Zakiyah	Afiliasi tidak diketahui	1
Agus Yodi Gunawan	Afiliasi tidak diketahui	1
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Sumber metadata: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai, pertama di-harvest 5 Nov 2026, terakhir terlihat 5 Nov 2026.

Metadata asli (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:format>application/pdf</dc:format>
	<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/6942</dc:identifier>
	<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>
	<dc:relation>10.20956/j.v16i3.6942.g5097</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2020 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
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