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Mathematical Study of an Inflammatory Model for Atherosclerosis: A Nonlinear Renewal Equation

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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.

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Authors and Affiliations

  1. MAP5, CNRS UMR 8145, Université Paris Descartes, 45 rue des Saints Pères, 75006, Paris, France

    Nicolas Meunier & Nicolas Muller

  2. LaMME, CNRS UMR 8071, Université d’Evry Val d’Essonne, 23 Boulevard de France, 91037, Evry Cedex, France

    Nicolas Meunier

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  1. Nicolas Meunier
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  2. Nicolas Muller
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Correspondence to Nicolas Meunier.

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Meunier, N., Muller, N. Mathematical Study of an Inflammatory Model for Atherosclerosis: A Nonlinear Renewal Equation. Acta Appl Math 161, 107–126 (2019). https://doi.org/10.1007/s10440-018-0206-x

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  • DOI: https://doi.org/10.1007/s10440-018-0206-x

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