ASYMPTOTIC STABILITY FOR A FREE BOUNDARY MODEL OF AN ATHEROSCLEROTIC PLAQUE FORMATION IN THE PRESENCE OF REVERSE CHOLESTEROL TRANSPORT WITH HOLLING TYPE-III FUNCTIONAL RESPONSE

Abstract

Atherosclerosis, as a chronic inflammatory disease, has been a threat to human health. How to diagnose and prevent this disease has long been the focus of medical and biomathematics study. In this paper, we investigate a free boundary model of an atherosclerotic plaque formation in the presence of reverse cholesterol transport, which includes low-density lipoprotein, high-density lipoprotein, endothelial stimulating cytokines, pro-inflammatory and anti-inflammatory macrophages, as well as foam cells. For this model, we use the Holling type-III response function instead of the usual Holling type-II to describe the change of the concentration of each substance. We first introduce the auxiliary function [Formula: see text] to prove the existence and uniqueness of small radially symmetric stationary plaque for appropriate [Formula: see text] and [Formula: see text] by using the contraction mapping principle and maximum principle, and then establish a condition to ensure their asymptotic stability behavior by expanding the corresponding steady-state solution.