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Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Mathematical Analysis of a Clonal Evolution Model of Tumour Cell Proliferation
Author(s): Farkas, Jozsef Zoltan
Webb, Glenn F
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Keywords: Cancer modelling
structured populations
semigroups of operators
asymptotic behaviour
telomere self-renewal
Issue Date: Mar-2017
Citation: Farkas JZ & Webb GF (2017) Mathematical Analysis of a Clonal Evolution Model of Tumour Cell Proliferation, Journal of Evolution Equations, 17 (1), pp. 275-308.
Abstract: We investigate a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which is applicable to the clonal evolution model of cancer cell growth. This model has a non-standard non-local boundary condition. We establish global existence of solutions and study their qualitative behaviour. We study the effect of telomere restoration on cancer cell dynamics. Our results indicate that without telomere restoration, the cell population extinguishes. With telomere restoration, exponential growth occurs in the linear model. We further characterise the specific growth behaviour of the cell population for special cases. We also study the effects of crowding induced mortality on the qualitative behaviour, and the existence and stability of steady states of a nonlinear model incorporating crowding effect. We present examples and extensive numerical simulations, which illustrate the rich dynamic behaviour of the linear and nonlinear models.
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