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ANALYSIS AND SIMULATION OF THE SIR MODEL ON THE SPREAD OF COVID-19 BY CONSIDERING THE VACCINATION FACTOR

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 18 No. 1 (2024) · pp. 0303–0312

DOI
10.30598/barekengvol18iss1pp0303-0312
ISSN
2615-3017, 1978-7227
Published
2024-03-01
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

Covid-19 is a serious respiratory disease that can be fatal for those affected. Governments have tried various strategies to conquer the Covid-19 pandemic. One of them is to vaccinate people with 6 years old and over. The vaccination program aims to form herd immunity so that the number of confirmed positive cases can be reduced. The purpose of this research is to form a mathematical model of the SIR (Susceptible-Infected-Recovery) spread of Covid-19 by considering vaccination factors. The SIR model is combined with a vaccination factor to forestall the unfold of Covid-19. The research method includes deriving models of nonlinear differential equation systems, solving qualitative models, deriving the basic reproduction ratio ( ), analysis of equilibrium points, and building simulation models. This model has an asymptotically stable disease-free equilibrium point. At the same time, the endemic equilibrium point is unstable. Model simulation is obtained by using different parameter values. This is proven through the outcomes of the model analysis vaccination coverage is a key parameter that can be controlled to reduce so that the pandemic ends soon.

Collaboration network of the authors

9 authors · 18 co-authorship links · 3 across different organisations

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  • Institut Teknologi Telkom Purwokerto
  • Universitas Gadjah Mada
  • National Research and Innovation Agency
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Nurlaili NurlailiInstitut Teknologi Telkom Purwokerto2
Hadi SusantoNational Research and Innovation Agency1
Nanang SusyantoUniversitas Gadjah Mada1
Lina AryatiAffiliation 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://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 8 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">ANALYSIS AND SIMULATION OF THE SIR MODEL ON THE SPREAD OF COVID-19 BY CONSIDERING THE VACCINATION FACTOR</dc:title>
	<dc:creator>Dewi, Atika Ratna</dc:creator>
	<dc:creator>Ananda, Ridho</dc:creator>
	<dc:creator>Rifanti, Utti Marina</dc:creator>
	<dc:creator>Anggraeni, Nadia Putri</dc:creator>
	<dc:creator>Ardian, Miko</dc:creator>
	<dc:description xml:lang="en-US">Covid-19 is a serious respiratory disease that can be fatal for those affected. Governments have tried various strategies to conquer the Covid-19 pandemic. One of them is to vaccinate people with 6 years old and over. The vaccination program aims to form herd immunity so that the number of confirmed positive cases can be reduced. The purpose of this research is to form a mathematical model of the SIR (Susceptible-Infected-Recovery) spread of Covid-19 by considering vaccination factors. The SIR model is combined with a vaccination factor to forestall the unfold of Covid-19. The research method includes deriving models of nonlinear differential equation systems, solving qualitative models, deriving the basic reproduction ratio ( ), analysis of equilibrium points, and building simulation models. This model has an asymptotically stable disease-free equilibrium point. At the same time, the endemic equilibrium point is unstable. Model simulation is obtained by using different parameter values. This is proven through the outcomes of the model analysis vaccination coverage is a key parameter that can be controlled to reduce  &amp;nbsp;so that the pandemic ends soon.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2024-03-01</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://ojs3.unpatti.ac.id/index.php/barekeng/article/view/10330</dc:identifier>
	<dc:identifier>10.30598/barekengvol18iss1pp0303-0312</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application; 0303-0312</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol18iss1year2024</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/10330/7543</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2024 Atika Ratna Dewi, Ridho Ananda, Utti Marina Rifanti, Nadia Putri Anggraeni, Miko Ardian</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
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