Electron. J. Diff. Eqns., Vol. 2003(2003), No. 107, pp. 1-14.

A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells

Mostafa Adimy & Laurent Pujo-Menjouet

In this paper, we investigate a linear population model of cells that are capable of simultaneous proliferation and maturation. We consider the case when the time required for a cell to divide depends on its maturity. This model is described by first order partial differential system with a retardation of the maturation variable and a time delay depending on this maturity. Both delays are due to cell replication.

Submitted February 14, 2003. Published October 23, 2003.
Math Subject Classifications: 35F15, 35L60, 92C37, 92D25.
Key Words: Structured population, cell cycle, stem cells, first order partial differential equation with delays, non constant delay.

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Mostafa Adimy
Departement de Mathematiques Appliquees
I.P.R.A., Universite de Pau
Avenue de l'universite, 64000
Pau, France
email: mostafa.adimy@univ-pau.fr
Laurent Pujo-Menjouet
Department of Physiology, Physics and Mathematics
Centre for Nonlinear dynamics, McGill University
3655 Drummond Street
Montreal, Quebec, Canada H3G 1Y6
email: pujo@cnd.mcgill.ca

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