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MATHEMATICAL MODEL OF THE SPREAD OF HIV/AIDS CONSIDERING THE LEVEL OF IMMUNITY

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 20 No. 1 (2025) · pp. 0211–0226

DOI
10.30598/barekengvol20iss1pp0211-0226
ISSN
2615-3017, 1978-7227
Published
2025-11-24
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

The immune system, crucial for defending the body against infections, is a primary target of HIV, compromising its ability to resist illnesses that may progress to AIDS. This study develops a mathematical model incorporating the immune response to simulate HIV/AIDS transmission dynamics. The model analysis includes the determination of equilibrium points, the basic reproduction number, and bifurcation behavior. Two equilibrium points are identified: the disease-free and endemic equilibria. The disease-free equilibrium is asymptotically stable when, while the endemic equilibrium is stable when, indicating persistent transmission. A forward bifurcation occurs at, which biologically implies that reducing below one is critical for eliminating the disease. Numerical simulations using actual data yield an estimated with a Mean Absolute Percentage Error (MAPE) of 4.5583%, indicating good agreement between the model and data. Although the model assumes homogeneous mixing and constant parameters, it provides meaningful insights into HIV/AIDS transmission and offers a quantitative basis for evaluating control strategies.

Collaboration network of the authors

8 authors · 14 co-authorship links · 6 across different organisations

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  • Sebelas Maret University
  • Universitas Ahmad Dahlan
  • University of Nusa Cendana
  • Different organisations
  • Same organisation
  • Affiliation unknown
  • Thicker line = more joint articles · bigger circle = more articles
Show as table
Co-authorOrganisationJoint articles
Meksianis Zadrak NdiiUniversity of Nusa Cendana1
Bertha Selviana DjahiUniversity of Nusa Cendana1
Laila FitrianaSebelas Maret University1
Ario WirayaSebelas Maret University1
Triyanto TriyantoSebelas Maret University1
Amellia PutriSebelas Maret University1

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">MATHEMATICAL MODEL OF THE SPREAD OF HIV/AIDS CONSIDERING THE LEVEL OF IMMUNITY</dc:title>
	<dc:creator>Linarta, Anisa Sukma</dc:creator>
	<dc:creator>Adi, Yudi Ari</dc:creator>
	<dc:description xml:lang="en-US">The immune system, crucial for defending the body against infections, is a primary target of HIV, compromising its ability to resist illnesses that may progress to AIDS. This study develops a mathematical model incorporating the immune response to simulate HIV/AIDS transmission dynamics. The model analysis includes the determination of equilibrium points, the basic reproduction number , and bifurcation behavior. Two equilibrium points are identified: the disease-free and endemic equilibria. The disease-free equilibrium is asymptotically stable when , while the endemic equilibrium is stable when , indicating persistent transmission. A forward bifurcation occurs at , which biologically implies that reducing &amp;nbsp;below one is critical for eliminating the disease. Numerical simulations using actual data yield an estimated &amp;nbsp;with a Mean Absolute Percentage Error (MAPE) of 4.5583%, indicating good agreement between the model and data. Although the model assumes homogeneous mixing and constant parameters, it provides meaningful insights into HIV/AIDS transmission and offers a quantitative basis for evaluating control strategies.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2025-11-24</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/17809</dc:identifier>
	<dc:identifier>10.30598/barekengvol20iss1pp0211-0226</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application; 0211-0226</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol20iss1year2026</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/17809/11704</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2025 Anisa Sukma Linarta, Yudi Ari Adi</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
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