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Qualitative Analysis of a PDE Model of Telomere Loss in a Proliferating Cell Population in the Light of Suns and Stars

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Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics

Abstract

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(u t). 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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Author information

Authors and Affiliations

  1. Faculty of Sciences, Department of Mathematics, Mohammed V University, Agdal, Rabat, Morocco

    Y. Elalaoui

  2. International University of Rabat, Sala Al-Jadida, Morocco

    L. Alaoui

Authors
  1. Y. Elalaoui
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  2. L. Alaoui
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Editor information

Editors and Affiliations

  1. Federal University of Rio de Janeiro, President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Elalaoui, Y., Alaoui, L. (2019). Qualitative Analysis of a PDE Model of Telomere Loss in a Proliferating Cell Population in the Light of Suns and Stars. In: Mondaini, R. (eds) Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-23433-1_6

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