Cross-Chemotaxis System Derived from an Atherosclerotic Plaque Model

TL;DR

This paper introduces a simplified mathematical model of chemotactic interactions between two cell types involved in arterial plaque formation, analyzing its mathematical properties and behaviors.

Contribution

It presents a reduced subsystem model of chemotactic cell interactions in atherosclerosis, with proofs of positivity and existence of solutions.

Findings

Proved positivity of solutions

Established local and global existence

Discussed qualitative behaviors of the system

Abstract

In modeling the inflammatory response to a lesion in an artery wall, there are a number of chemotactic mechanisms going on within the wall layer that lead to an arterial plaque. We introduce a rather reduced model of these dynamic processes, but the focus of this paper is a subsystem of the full model system that has independent interest. Namely, the system here consists of two cell densities, each producing a chemical that is a chemoattractant for the other cell type. Then we prove positivity, local and global existence, and discuss some qualitative behavior of solutions.