Dynamical behavior of a mathematical model of early atherosclerosis

Atherosclerosis,a continual inflammatory disease occurring due to plaque cumulation in the arterial intima,is one of the main reasons behind deaths from diverse cardiovascular diseases.The basic interactions between oxidized low density lipoprotein(LDL)and macrophages in the formation of atherosclerotic plaque are modeled here in terms of a reaction-diffusion system in one-dimensional(1D)space under Neumann boundary conditions.Two simple mathematical models are considered which differ by the influx term only in the case of the interaction of oxidized LDL.Both the spatial and nonspatial systems are simply analyzed theoretically and numerically.Numerical bifurcation analysis confirms the existence of Hopf bifurcation concerning four significant model parameters.Examining the gravity of the model offered in this investigation,an obvious insight into this inflammatory response can be achieved both qualitatively and quantitatively.