Stability Analysis of a Renewal Equation for Cell Population Dynamics with Quiescence

We propose a model to analyze the dynamics of interacting proliferating and quiescent cell populations. The model includes age dependence of cell division, transitions between the two sub-populations and regulation of the recruitment of quiescent cells. We formulate the model as a pair of renewal equations and apply a rather recent general result to prove that (in-)stability of equilibria can be analyzed by locating roots of characteristic equations. We are led to a parameter plane analysis of a characteristic equation, which has not been analyzed in this way so far. We conclude how quiescence of cells as well as two sub-models for cell-division may influence the possibility of destabilization via oscillations.