American Institute of Mathematical Sciences

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2011, 2011(Special): 32-43. doi: 10.3934/proc.2011.2011.32

A model for stem cell population dynamics with regulated maturation delay

Tomas Alarcon 1, , Philipp Getto 2, , Anna Marciniak-Czochra 3, and  Maria dM Vivanco 4,

1. 

Centre de Recerca Matem, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain
2. 

BCAM (Basque Center For Applied Mathematics), Bizkaia Technology Park, Building 500, E-48160 Derio, Spain
3. 

University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR), Institute of Applied Mathematics and BIOQUANT, Im Neuenheimer Feld 267, 69120 Heidelberg
4. 

CIC BioGUNE, Bizkaia Technology Park, Building 801 A, E-48160 Derio, Spain

Received  July 2010 Revised  April 2011 Published  September 2011

We develop a structured population model for the maturation process of stem cells in the form of a state-dependent delay di erential equation. Moreover, results on existence, uniqueness and positivity of solutions as well as conditions of existence for equilibria and representations of these are established. We give biological interpretations for the conditions of existence of equilibria.
Keywords: state-dependent delay di erential equation, stem cells, structured population model.
Mathematics Subject Classification: Primary: 34K05; Secondary: 92B05.
Citation: Tomas Alarcon, Philipp Getto, Anna Marciniak-Czochra, Maria dM Vivanco. A model for stem cell population dynamics with regulated maturation delay. Conference Publications, 2011, 2011 (Special) : 32-43. doi: 10.3934/proc.2011.2011.32
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