Qualitative Analysis of a PDE Model of Telomere Loss in a Proliferating Cell Population in the Light of Suns and Stars
A model describing the interactions between cells of several levels of differentiation and malignancy by tracking their lineages while taking into consideration the proliferation process is analyzed. The model is structured by age and is formulated by a system of partial differential equations. 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 compactness and spectral properties are established to conclude the asynchronous exponential growth property for the model and the characterization of associated Malthusian coefficient by only using the properties of ϕ.
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