Cross-Chemotaxis System Derived from an Atherosclerotic Plaque Model

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.