Asymptotic behavior of an integral equation of cell cycle model in the light of suns and stars

In this paper a model of cell proliferation with unequal division is analyzed. The model uses an integral equation to describe the dynamics of the cells density. The analysis of the model is done using tools of the theory developed for the class of perturbed dual semigroups that are solutions of an abstract integral equation. Existence, uniqueness, positivity, compactness and spectral properties of the solution semigroup are derived in order to conclude the asynchronous exponential growth property for the model.