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 qua...

This paper presents two simple models for nonlinear age-dependent population dynamics. In these models the basic equations of the theory reduce to systems of ordinary differential equations. We discuss certain qualitative aspects of these systems; in particular, we show that for many cases of interest periodic solutions are not possible. 1. BASIC EQUATIONS Recently, Gurtin and MacCamy [l] intro...

One way of modeling the evolution in time of an age-structured population is to set up the evolution process as a partial diierential equation in which time and age are the independent variables. The resulting equation, known as the McKendrick equation, has received attention recently from mathematicians. Some advantages of the PDE are that it can easily be adapted to include more detail in the...