Abstract:
Atherosclerosis is an inflammatory disease that involves the accumulation of lipid
deposits, cholesterol, and several other substances within the arterial wall. This
buildup of what is known as the atherosclerotic plaque hardens and narrows the
blood vessels, constricting the blood flow and causing heart attacks and strokes.
In this work, we model the inflammatory stage of this disease through a system
of reaction-diffusion partial differential equations. Low density lipoproteins
(LDL), free radicals, oxidized low density lipoproteins (ox-LDL), macrophages,
and pro-inflammatory cytokines are the main key role players that are taken into
consideration. The stability analysis of the corresponding ODE system is performed
and studied in detail. We then focus on proving the existence of traveling
wave solutions of the system. In addition, we establish biological insights from
the mathematical study, illustrated by numerical simulations. Finally, we emphasize
the role of the rate of oxidation of LDL, which is an important factor in
the set-up of this inflammatory disease.
