  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.

Analysis of PDEs;Populations and Evolution