The authors analyze a linear model of cell population dynamics structured by age (denoted a) with two interacting compartments: proliferating cells (with densities and quiescent cells (with densities ; is time. The equations of the model are:
where is the division rate, is the transition rate from the proliferating stage to the quiescent stage, is the transition rate from the quiescent stage to the proliferating stage, and is maximal age of division.
Necessary and sufficient conditions are established for the population to exhibit asymptotic behavior of asynchronous exponential growth. The model is analyzed as a semigroup of linear operators.