Skip to Main content Skip to Navigation
Habilitation à diriger des recherches

Equations à Retard et Modèles de Dynamiques de Populations Cellulaires

Fabien Crauste 1, 2
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : I present my research activity from 2006, when I have been recruited by the CNRS, throughout two chapters. It deals with the modeling and mathematical study of biological processes associated with cell dynamics and involving regulations of the considered mechanisms. The processes as well as the regulatory mechanisms deal with different physical and temporal scales, so the works I present evolve from the study of “mono”-scale problems to multiscale problems. Although theoretical works and applications are presented separately, they are usually dealt with simultaneously. The current presentation aims atstressing both theoretical and applied contributions. In the first chapter, I present the results obtained while qualitatively studying delay equations and age structured partial differential equations. I focus on the asymptotic stability analysis of delay equations for discrete, continous distributed, and state-dependent delays, and I present the most relevant results in these three cases. Global stability for such equations is briefly discussed. In the second chapter, I present biological applications that motivated the theoretical works presented in the first chapter. I begin with the study of hematopoietic stem cell dynamics, a work started during my PhD thesis and carried on for few years. I then move to the presentation of the works on the modeling of erythropoiesis and the immune response, both performed in close collaboration with biologists from Lyon. In both cases, the relevance of the results is presented with respect to biological questions of interest and to theoretical answers that have been brought.
Document type :
Habilitation à diriger des recherches
Complete list of metadata
Contributor : Fabien Crauste <>
Submitted on : Tuesday, December 9, 2014 - 2:13:14 PM
Last modification on : Monday, June 28, 2021 - 2:26:03 PM
Long-term archiving on: : Saturday, April 15, 2017 - 4:36:25 AM


  • HAL Id : tel-01092352, version 1


Fabien Crauste. Equations à Retard et Modèles de Dynamiques de Populations Cellulaires. Mathématiques générales [math.GM]. Université Claude Bernard Lyon 1, 2014. ⟨tel-01092352⟩



Record views


Files downloads