BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application

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

Linarta, Anisa Sukma (Unknown)
Adi, Yudi Ari (Unknown)



Article Info

Publish Date
24 Nov 2025

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.

Copyrights © 2026






Journal Info

Abbrev

barekeng

Publisher

Subject

Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

Description

BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure ...