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STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 19 No. 1 (2025) · pp. 173–184

DOI
10.30598/barekengvol19iss1pp173-184
ISSN
2615-3017, 1978-7227
Published
2025-01-13
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

Diphtheria is an acute disease that affects the upper respiratory tract caused by Corynebacterium diphtheriae, which can also affect the skin, eyes, and other organs. This article analyzes the stability of the SIQR model of diphtheria disease spread in Mandau District by considering the migration factor. The SIQR model is a development of the SIR model by incorporating the quarantine process as an alternative to reduce morbidity. The purpose of this study is to see the effect of migration on the spread of diphtheria disease in Mandau District through mathematical model simulation. We calculated the disease-free and endemic equilibrium points and the basic reproduction number ( ) of the model. Model parameters were obtained using data from BPS Bengkalis Regency and UPTD Puskesmas Mandau. The calculation resulted in one disease-free equilibrium point and one endemic equilibrium point. If 1, then the endemic equilibrium point is also asymptotically stable. Based on the results of the data analysis, the value of. This value is less than 1, so the equilibrium point obtained is a disease-free and asymptotically stable equilibrium point. This means that the population will be free from diphtheria and the level of migration affects the presence of diphtheria disease in Mandau District.

Collaboration network of the authors

14 authors · 25 co-authorship links

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  • State University of Malang
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
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Co-authorOrganisationJoint articles
Yuslenita MudaAffiliation unknown3
Eko SujarwantoState University of Malang1
Arif HidayatState University of Malang1
Rinda KiranaAffiliation unknown1
Muhafzan MuhafzanAffiliation unknown1
Neng SantiAffiliation unknown1
Ermawati ErmawatiAffiliation unknown1
Idhia SrilianaAffiliation unknown1
Irma SuryaniAffiliation 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 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">STABILITY ANALYSIS OF THE SIQR MODEL OF DIPHTHERIA DISEASE SPREAD AND MIGRATION IMPACT</dc:title>
	<dc:creator>Soleh, Mohammad</dc:creator>
	<dc:creator>Nazvira, Mutia</dc:creator>
	<dc:creator>Wartono, Wartono</dc:creator>
	<dc:creator>Safitri, Elfira</dc:creator>
	<dc:creator>Sriningsih, Riry</dc:creator>
	<dc:description xml:lang="en-US">Diphtheria is an acute disease that affects the upper respiratory tract caused by Corynebacterium diphtheriae, which can also affect the skin, eyes, and other organs. This article analyzes the stability of the SIQR model of diphtheria disease spread in Mandau District by considering the migration factor. The SIQR model is a development of the SIR model by incorporating the quarantine process as an alternative to reduce morbidity. The purpose of this study is to see the effect of migration on the spread of diphtheria disease in Mandau District through mathematical model simulation. We calculated the disease-free and endemic equilibrium points and the basic reproduction number ( ) of the model. Model parameters were obtained using data from BPS Bengkalis Regency and UPTD Puskesmas Mandau. The calculation resulted in one disease-free equilibrium point and one endemic equilibrium point. If  &amp;nbsp;&amp;lt; 1, then the disease-free equilibrium point is asymptotically stable, and if  &amp;nbsp;&amp;gt; 1, then the endemic equilibrium point is also asymptotically stable. Based on the results of the data analysis, the value of. This value is less than 1, so the equilibrium point obtained is a disease-free and asymptotically stable equilibrium point. This means that the population will be free from diphtheria and the level of migration affects the presence of diphtheria disease in Mandau District.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-01-13</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/13060</dc:identifier>
	<dc:identifier>10.30598/barekengvol19iss1pp173-184</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 19 No 1 (2025): BAREKENG: Journal of Mathematics and Its Application; 173-184</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol19iss1year2025</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/13060/9509</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Mohammad Soleh, Mutia Nazvira, Wartono Wartono, Elfira Safitri, Riry Sriningsih</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
</oai_dc:dc>