| Issue |
Math. Model. Nat. Phenom.
Volume 20, 2025
Special Issue to honour Vitaly's work
|
|
|---|---|---|
| Article Number | 19 | |
| Number of page(s) | 20 | |
| DOI | https://doi.org/10.1051/mmnp/2025018 | |
| Published online | 10 July 2025 | |
A Qualitative Analysis of the Inflammatory Response in Atherosclerosis with Emphasis on LDL Oxidation
1
Lebanese American University, Department of Computer Science and Mathematics, Byblos, Lebanon.
2
Universite Claude Bernard Lyon 1, CNRS, Ecole Centrale de Lyon, INSA Lyon, Universit´e Jean Monnet, ICJ UMR5208, 69622 Villeurbanne, France.
* Corresponding author: nader.elkhatib@lau.edu.lb
Received:
30
October
2024
Accepted:
28
May
2025
Inflammation plays a major factor in the development of atheroscls, highlighted by the buildup of fats on arterial walls. In this work, we model the inflammatory stage of this disease through a system of partial differential equations. Low density lipoproteins (LDL), free radicals, oxidized low density lipoproteins (ox-LDL), macrophages and pro-inflammatory cytokines are taken into consideration. The stability analysis of the corresponding ODE system is studied in details. Then, we focus on proving the existence of traveling wave solutions. Moreover, we establish biological insights of the mathematical study that is illustrated by numerical simulations. Finally, we highlight the role of the oxidation rate of LDL as an important step in the set-up of this inflammatory disease.
Mathematics Subject Classification: 35K57 / 35C07 / 92C32
Key words: Inflammation / reaction-diffusion equations / atherosclerosis / wave existence
© The authors. Published by EDP Sciences, 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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