A Kinetics Model of Amyloid-Beta (Aβ) in Alzheimer’s Disease Using Euler and Fourth-order Runge-Kutta Methods

Authors

  • Cindyawati Cindyawati Departement of Physics, Faculty of Sciences, Parahyangan Catholic University, Jalan Ciumbuleuit no. 94, Gedung 9, Bandung 40141, Indonesia
  • Faozan Ahmad Departement of Physics, Faculty of Mathematical and Natural Sciences, IPB University (Bogor Agricultural University), Jalan Meranti, Building Wing S, 2nd Floor, Kampus IPB Dramaga, Bogor 16680, Indonesia
  • Hendradi Hardhienata Departement of Physics, Faculty of Mathematical and Natural Sciences, IPB University (Bogor Agricultural University), Jalan Meranti, Building Wing S, 2nd Floor, Kampus IPB Dramaga, Bogor 16680, Indonesia
  • Agus Kartono Departement of Physics, Faculty of Mathematical and Natural Sciences, IPB University (Bogor Agricultural University), Jalan Meranti, Building Wing S, 2nd Floor, Kampus IPB Dramaga, Bogor 16680, , Indonesia

DOI:

https://doi.org/10.25077/jif.17.2.125-134.2025

Keywords:

Amyloid-beta (Aꞵ), Alzheimer disease , Euler Method, Runge-Kutta Method, Mathematical model

Abstract

Alzheimer's disease (AD) is a neurological disease that causes decreased brain function. It is known that the accumulation of amyloid-beta (Aβ) plaques in the brain is one of the causes of AD. The accumulation of Aβ plaques in the brain is a dynamic process; it begins with the growth of amyloid-beta monomers (M1). Furthermore, amyloid-beta dimers (M2) and so on, so that this collected into oligomers (O), fibrils (P), and plaques in the brain. This disrupts the communication pathways between nerve cells. In this study, each process of amyloid-beta plaque accumulation is presented with a mathematical model in the form of an ordinary differential equation. Therefore, the coupled ordinary differential equations are given for the entire process of Aβ plaque accumulation. In this study, this coupled model is calculated using numerical methods, such as the Euler and fourth-order Runge-Kutta methods. The Euler methods is simple and efficient, but its accuracy is low and can accumulate errors with larger step sizes. The fourth-order Runge-Kutta methods offers higher accuracy, better numerical stability, and greater control over the accuracy of the solution. These two numerical methods have never been compared for estimating numerical solutions of coupled ordinary differential equations.

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Published

2025-05-13

How to Cite

Cindyawati, C., Ahmad, F., Hardhienata, H., & Kartono, A. (2025). A Kinetics Model of Amyloid-Beta (Aβ) in Alzheimer’s Disease Using Euler and Fourth-order Runge-Kutta Methods. JURNAL ILMU FISIKA | UNIVERSITAS ANDALAS, 17(2), 125–134. https://doi.org/10.25077/jif.17.2.125-134.2025

Issue

Vol. 17 No. 2 (2025): September 2025

Section

Research Article

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Copyright (c) 2025 Cindyawati Cindyawati, Faozan Ahmad, Hendradi Hardhienata, Agus Kartono

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