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SEIPR-Mathematical Model of the Pneumonia Spreading in Toddlers with Immunization and Treatment Effects

Jurnal Matematika, Statistika dan Komputasi · Vol. 17 No. 2 (2020) · pp. 202–218

DOI
10.20956/jmsk.v17i2.11166
ISSN
2614-8811, 1858-1382
Published
2020-12-23
Publisher
Department of Mathematics, Hasanuddin University
Language
en
License
creativecommons.org/licenses/by/4.0

Abstract

This research discussed the SEIPR mathematical model on the spread of pneumonia among children under five years old. The development of the model was done by considering factors of immunization and treatment factors, in an effort to reduce the rate of spread of pneumonia. In this research, mathematical model construction, stability analysis, and numerical simulation were carried out to see the dynamics of pneumonia cases in the population. The model analysis produces two equilibrium points, which are the equilibrium point without the disease, the endemic equilibrium point, and the basic reproduction number ( ) as the threshold value for disease spread. The point of equilibrium without disease reaches a stable state at the moment, which indicates that pneumonia will disappear from the population, while the endemic equilibrium point reaches a stable state at that time, which indicates that the disease will spread in the population. Furthermore, numerical simulations show that increasing the rate parameters of infected individuals undergoing treatment ( ), the treatment success rate ( ), and the immunization proportion ( ), could suppress the basic reproductive number so that control of the disease spread rate can be accelerated.

Keywords

Collaboration network of the authors

28 authors · 78 co-authorship links

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  • Universitas Halu Oleo
  • Institut Agama Islam Muhammadiyah Sinjai
  • State University of Semarang
  • State University of Gorontalo
  • Affiliation unknown
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Lailany YahyaAffiliation unknown4
La Ode NasharAffiliation unknown3
R. ResmawanAffiliation unknown2
Dewi Rahmawaty IsaAffiliation unknown2
Sri Lestari MahmudAffiliation unknown2
Gusti Arviana RahmanUniversitas Halu Oleo2
Syarif AbdullahAffiliation unknown2
Sri Istiyarti Uswatun ChasanahAffiliation unknown2
Nina ValentikaAffiliation unknown2
Sri Adiningsi B. UsmanAffiliation unknown1
Nurwan NurwanAffiliation unknown1
Moh Rizal HusainAffiliation unknown1
Isran R. OliiAffiliation unknown1
Nur Safitri AbdulAffiliation unknown1
Nazrilla Hasan LaitaAffiliation unknown1
Asriadi AsriadiInstitut Agama Islam Muhammadiyah Sinjai1
Amanda AdityaningrumAffiliation unknown1
Annisa Maharani BrahimAffiliation unknown1
Agus SuryantoState University of Semarang1
Hasan S. PanigoroAffiliation unknown1
Isnani DartiAffiliation unknown1
Emli RahmiState University of Gorontalo1
Nurhalis HasanAffiliation unknown1
Melasarah Deswita RahmadiAffiliation 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://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">SEIPR-Mathematical Model of the Pneumonia Spreading in Toddlers with Immunization and Treatment Effects</dc:title>
	<dc:creator xml:lang="en">Imran, Rusniwati S.</dc:creator>
	<dc:creator xml:lang="en">Resmawan, Resmawan</dc:creator>
	<dc:creator xml:lang="en">Achmad, Novianita</dc:creator>
	<dc:creator xml:lang="en">Nuha, Agusyarif Rezka</dc:creator>
	<dc:subject xml:lang="en">Pneumonia</dc:subject>
	<dc:subject xml:lang="en">SEIPR Mathematical Model</dc:subject>
	<dc:subject xml:lang="en">Equilibrium Point</dc:subject>
	<dc:subject xml:lang="en">Basic Reproduction Number</dc:subject>
	<dc:description xml:lang="en">This research discussed the SEIPR mathematical model on the spread of pneumonia among children under five years old. The development of the model was done by considering factors of immunization and treatment factors, in an effort to reduce the rate of spread of pneumonia. In this research, mathematical model construction, stability analysis, and numerical simulation were carried out to see the dynamics of pneumonia cases in the population. The model analysis produces two equilibrium points, which are the equilibrium point without the disease, the endemic equilibrium point, and the basic reproduction number ( ) as the threshold value for disease spread. The point of equilibrium without disease reaches a stable state at the moment , which indicates that pneumonia will disappear from the population, while the endemic equilibrium point reaches a stable state at that time , which indicates that the disease will spread in the population. Furthermore, numerical simulations show that increasing the rate parameters of infected individuals undergoing treatment ( ), the treatment success rate ( ), and the immunization proportion ( ), could suppress the basic reproductive number so that control of the disease spread rate can be accelerated.</dc:description>
	<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
	<dc:date>2020-12-23</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/11166</dc:identifier>
	<dc:identifier>10.20956/jmsk.v17i2.11166</dc:identifier>
	<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 17 No. 2 (2021): JANUARY 2021; 202-218</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/11166/6171</dc:relation>
	<dc:relation>10.20956/j.v17i2.11166.g6171</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2020 Author and publisher</dc:rights>
	<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>