A model for stem cell population dynamics with regulated maturation delay

Pages: 32 - 43, Issue Special, September 2011

 Abstract        Full Text (477.0K)              

Tomas Alarcon - Centre de Recerca Matem, Campus de Bellaterra, Edifici C, 08193 Bellaterra, Barcelona, Spain (email)
Philipp Getto - BCAM (Basque Center For Applied Mathematics), Bizkaia Technology Park, Building 500, E-48160 Derio, Spain (email)
Anna Marciniak-Czochra - University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR), Institute of Applied Mathematics and BIOQUANT, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany (email)
Maria dM Vivanco - CIC BioGUNE, Bizkaia Technology Park, Building 801 A, E-48160 Derio, Spain (email)

Abstract: 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, structured population model, stem cells
Mathematics Subject Classification:  Primary: 34K05; Secondary: 92B05

Received: July 2010;      Revised: April 2011;      Published: September 2011.