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Stability analysis using an energy estimate approach of a reaction-diffusion model of atherogenesis. (English) Zbl 1194.35049

Summary: This paper considers modeling the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Russell Ross, atherogenesis is viewed as an inflammatory spiral with positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammation is modeled through a system of nonlinear reaction/diffusion/convection partial differential equations. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Conditions on system parameters guaranteeing stability of the health state and conditions on system parameters leading to instability are given. Among the questions addressed in the analysis is the possible mitigating effect of anti-oxidants upon transition to the inflammatory spiral.

MSC:

35B35 Stability in context of PDEs
92C17 Cell movement (chemotaxis, etc.)
92C50 Medical applications (general)
35K58 Semilinear parabolic equations
35K51 Initial-boundary value problems for second-order parabolic systems
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