Analysis and numerical simulation of a reaction–diffusion mathematical model of atherosclerosis

Atherosclerosis is a chronic inflammatory disease which occurs due to plaque accumulation in the intima, the innermost layer of the artery. In this paper, a simple reaction–diffusion mathematical model of the plaque formation process comprising of oxidized LDL and macrophages has been developed. Linear stability analysis of the non-spatial model leads to the existence of global stability of the kinetic system. This reveals that the non-spatial system can withstand a substantial change in the significant model parameter values which can be taken forward for further clinical investigations. Numerical bifurcation analysis of the non-spatial system confirms the existence of Hopf bifurcation with respect to two significant model parameters. The biological importance of these bifurcation diagrams is discussed in detail. The significance of the model presented in this research paper provides a clear insight into the role of the key constituents, oxidized LDL and macrophages, involved in the plaque-forming process.