Stability Analysis of a Mathematical Model of Atherosclerotic Plaque Development: Fibrous Cap Formation and Degradation

Abstract

Atherosclerosis is an inflammatory disease in which plaque builds up in the artery wall. The growth of atherosclerotic plaque leads to the narrowing of the blood vessel, which may result in many possible disorders, such as coronary heart disease, cardiovascular diseases, myocardial infarction and stroke. This paper proposed a mathematical model of the essential chemical processes associated with atherosclerotic plaque development, which concentrates on the formation and possible degradation of the fibrous cap. It was shown that, under suitable conditions for the system parameters, the model system admits positive solutions. Local stability of the equilibrium was proven and conditions on the system parameters provided that ensure the system’s global stability.