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We investigate a partial differential equation model of a cancer cellpopulation, which is structured with respect to age and telomere length ofcells. We assume a continuous telomere length structure, which is applicable tothe clonal evolution model of cancer cell growth. This model has a non-standardnon-local boundary condition. We establish global existence of solutions andstudy their qualitative behaviour. We study the effect of telomere restorationon cancer cell dynamics. Our results indicate that without telomererestoration, the cell population extinguishes. With telomere restoration,exponential growth occurs in the linear model. We further characterise thespecific growth behaviour of the cell population for special cases. We alsostudy the effects of crowding induced mortality on the qualitative behaviour,and the existence and stability of steady states of a nonlinear modelincorporating crowding effect. We present examples and extensive numericalsimulations, which illustrate the rich dynamic behaviour of the linear andnonlinear models.

Mathematical Analysis of a Clonal Evolution Model of Tumour Cell Proliferation