Modelling the inflammatory process in atherosclerosis: a nonlinear renewal equation - Archive ouverte HAL
Article Dans Une Revue Acta Applicandae Mathematicae Année : 2019

Modelling the inflammatory process in atherosclerosis: a nonlinear renewal equation

Résumé

We present here a population structured model to describe the dynamics of macrophage cells. The model involves the interactions between modified LDL, monocytes/macrophages, cytokines and foam cells. The key assumption is that the individual macrophage dynamics depends on the amount of lipoproteins it has internalized. The obtained renewal equation is coupled with an ODE describing the lipoprotein dynamics. We first prove global existence and uniqueness for the nonlinear and nonlocal system. We then study long time asymp-totics in a particular case describing silent plaques which undergo periodic rupture and repair. Finally we study long time asymptotics for the nonlinear renewal equation obtained when considering the steady state of the ODE. and we prove that ....
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Dates et versions

hal-01497868 , version 1 (29-03-2017)

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Nicolas Meunier, Nicolas Muller. Modelling the inflammatory process in atherosclerosis: a nonlinear renewal equation. Acta Applicandae Mathematicae, 2019, 161 (1). ⟨hal-01497868⟩
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