Mathematical analysis of an age structured multi phases cell cycle model with checkpoints

Abstract

A system of partial differential equations modelling the cell division by considering an age structure within a population of cells controlled by many complex regulatory mechanisms is analysed. The analysis of the model is based on the perturbation theory for dual semigroups of operators applied to a renewal equation of the type u(t) = ϕ(ut). The operator ϕ associated with the model is determined and various properties are established to conclude the AEG property associated to the PDE model. Furthermore, the associated Malthusian coefficient is characterized by only using properties of ϕ.