Steady solution and its stability of a mathematical model of diabetic atherosclerosis

Abstract

Atherosclerosis is a leading cause of death worldwide. Making matters worse, nearly 463 million people have diabetes, which increases atherosclerosis-related inflammation. Diabetic patients are twice as likely to have a heart attack or stroke. In this paper, we consider a simplified mathematical model for diabetic atherosclerosis involving LDL, HDL, glucose, insulin, free radicals (ROS), β cells, macrophages and foam cells, which satisfy a system of partial differential equations with a free boundary, the interface between the blood flow and the plaque. We establish the existence of small radially symmetric stationary solutions to the model and study their stability. Our analysis shows that the plague will persist due to hyperglycemia even when LDL and HDL are in normal range, hence confirms that diabetes increase the risk of atherosclerosis.

Keywords:

• Atherosclerosis
• diabetes
• free boundary problem
• steady solution
• stability

Mathematic Subject classifications:

• 35Q92
• 92C50

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Research reported in this paper was supported by National Institute of General Medical Sciences of the National Institutes of Health under Award Number UL1GM118973.