Mostafa Adimy & Laurent Pujo-Menjouet
Abstract:
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 |
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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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