An age-and-cyclin-structured cell population model for healthy and tumoral tissues

We present a nonlinear model of the dynamics of a cell population divided into proliferative and quiescent compartments. The proliferative phase represents the complete cell cycle (G 1−S−G 2−M) of a population committed to divide at its end. The model is structured by the time spent by a cell in the proliferative phase, and by the amount of Cyclin D/(CDK4 or 6) complexes. Cells can transit from one compartment to the other, following transition rules which differ according to the tissue state: healthy or tumoral. The asymptotic behaviour of solutions of the nonlinear model is analysed in two cases, exhibiting tissue homeostasis or tumour exponential growth. The model is simulated and its analytic predictions are confirmed numerically.