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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan
Anisa Sukma Linarta
Department of Mathematics, Faculty of Applied Science and Technology, Universitas Ahmad Dahlan, Indonesia
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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MATHEMATICAL MODEL OF THE SPREAD OF HIV/AIDS CONSIDERING THE LEVEL OF IMMUNITY Anisa Sukma Linarta; Yudi Ari Adi
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0211-0226

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.
Co-Authors Yudi Ari Adi