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Stability analysis of an atherosclerotic plaque formation model with time delay
  • Wenjun Liu,
  • Yonglin Chen,
  • Yongqing Zhao
Wenjun Liu
Nanjing University of Information Science and Technology

Corresponding Author:[email protected]

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Yonglin Chen
Nanjing University of Information Science and Technology
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Yongqing Zhao
Nanjing University of Information Science and Technology
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Abstract

Atherosclerosis is a chronic inflammatory disease that poses a serious threat to human health. It starts with the buildup of plaque in the artery wall, which results from the accumulation of pro-inflammatory factors and other substances. In this paper, we propose a mathematical model of early atherosclerosis with a free boundary and time delay. The time delay represents the transformation of macrophages into foam cells. We obtain an explicit solution and analyze the stability of the model and the effect of the time delay on plaque size. We show that for non-radial symmetric perturbations, when $n = 0$ or $1$, the steady-state solution $(M_*,p_*,r_*)$ is linearly stable; when $n \ge 2$, there exists a critical parameter $L_*$ such that the steady-state solution is linearly stable for $L < L_*$ and unstable for $L > L_*$. Moreover, we find that smaller plaque are associated with the presence of time delay.
07 Aug 2023Submitted to Mathematical Methods in the Applied Sciences
07 Aug 2023Submission Checks Completed
07 Aug 2023Assigned to Editor
11 Aug 2023Review(s) Completed, Editorial Evaluation Pending
17 Aug 2023Reviewer(s) Assigned
03 Nov 2023Editorial Decision: Revise Major
13 Nov 20231st Revision Received
15 Nov 2023Submission Checks Completed
15 Nov 2023Assigned to Editor
15 Nov 2023Review(s) Completed, Editorial Evaluation Pending
16 Nov 2023Reviewer(s) Assigned