1. Mathematical Study of an Inflammatory Model for Atherosclerosis: A Nonlinear Renewal Equation.
- Author
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Meunier, Nicolas and Muller, Nicolas
- Subjects
- *
NONLINEAR equations , *DIFFERENTIAL equations , *ORDINARY differential equations , *ATHEROSCLEROSIS , *LEUCOCYTES , *INFLAMMATION - Abstract
In this work we study the coupling of a nonlinear renewal equation to an ordinary differential equation. We start with existence and uniqueness issues for the coupled equations and, in particular cases, we study the long-time behaviour. The novelty here is the nonlinearity in the renewal equation. This model arises in the context of atherosclerosis. The renewal part accounts for the inflammatory process: leucocyte recruitment in the arterial wall, differentiation when internalizing low-density lipoprotein (LDL) and death. The ordinary differential equation describes the LDL dynamics in the arterial wall, leucocyte absorption and release in the blood. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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