The authors study an age-structured model for the growth of cell populations. Their model accounts for the transition between different phases in the cell cycle and for transitions between proliferating and quiescent stages. In quiescence the maturation stops. Reproduction is assumed to occur via mitosis. The authors show the existence and the exponential stability of a stationary normalized age-distribution. This stationary normalized age-distribution corresponds to an exponentially growing solution of the cell-population model, where all components grow at the same rate. This rate, and the rate of convergence towards it, are derived from the model parameters. For the proof of stability the authors use Laplace transform methods, since the method of characteristics is not applicable.
the asymptotic behaviour of a proliferant-quiescent cell system
GUIOTTO, PAOLO;
2000
Abstract
The authors study an age-structured model for the growth of cell populations. Their model accounts for the transition between different phases in the cell cycle and for transitions between proliferating and quiescent stages. In quiescence the maturation stops. Reproduction is assumed to occur via mitosis. The authors show the existence and the exponential stability of a stationary normalized age-distribution. This stationary normalized age-distribution corresponds to an exponentially growing solution of the cell-population model, where all components grow at the same rate. This rate, and the rate of convergence towards it, are derived from the model parameters. For the proof of stability the authors use Laplace transform methods, since the method of characteristics is not applicable.
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