A Qualitative Analysis of the Inflammatory Response in Atherosclerosis with Emphasis on LDL Oxidation

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.