AEG property of a cell cycle model with quiescence in the light of translation semigroups

Abstract A linear cell cycle model with cells either in a proliferating or a quiescent state is analyzed using the theory developed for the class of translation semigroups that are associated with a core operator φ and are solutions of equations of the type m(t) = φ(mt). This allows us to give properties of the solution semigroup of the model such as existence, uniqueness, positivity, compactness and spectral properties in order to conclude the asynchronous exponential growth property (AEG) for the model. In particular a characterization of the malthusian parameter in the AEG property is given and all established results are derived by only using properties of the model’s core operator.