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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) · hlm. 0211–0226

DOI
10.30598/barekengvol20iss1pp0211-0226
ISSN
2615-3017, 1978-7227
Terbit
2025-11-24
Penerbit
PATTIMURA UNIVERSITY
Bahasa
eng
Lisensi
creativecommons.org/licenses/by-sa/4.0

Abstrak

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.

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  • Sebelas Maret University
  • Universitas Ahmad Dahlan
  • University of Nusa Cendana
  • State University of Semarang
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  • Organisasi sama
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Tampilkan sebagai tabel
Rekan penulisOrganisasiArtikel bersama
Meksianis Zadrak NdiiUniversity of Nusa Cendana1
Bertha Selviana DjahiUniversity of Nusa Cendana1
Laila FitrianaSebelas Maret University1
Ario WirayaSebelas Maret University1
Triyanto TriyantoState University of Semarang1
Amellia PutriSebelas Maret University1

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Sumber metadata: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, pertama di-harvest 5 Nov 2026, terakhir terlihat 8 Nov 2026.
Metadata asli (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>
</oai_dc:dc>