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Delay equation formulation of a cyclin-structured cell population model

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Abstract

The aim of this paper is to derive a system of two renewal equations from individual-level assumptions concerning a cyclin-structured cell population. Nonlinearity arises from the assumption that the rate at which quiescent cells become proliferating is determined by feedback. In fact, we assume that this rate is a nonlinear function of a weighted population size. We characterize steady states and establish the validity of the principle of linearized stability.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra (Barcelona), Spain

    Ricardo Borges, Àngel Calsina & Sílvia Cuadrado

  2. Department of Mathematics, Utrecht University, Utrecht, The Netherlands

    Odo Diekmann

Authors
  1. Ricardo Borges
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  2. Àngel Calsina
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  3. Sílvia Cuadrado
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  4. Odo Diekmann
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Corresponding author

Correspondence to Sílvia Cuadrado.

Additional information

R. Borges, À. Calsina and S. Cuadrado were partially supported by the Ministerio de Ciencia e Innovación, Grant MTM2011-27739-C04-02, and by the Agència de Gestió d’Ajuts Universitaris i de Recerca-Generalitat de Catalunya, Grant 2009-SGR-345.

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Borges, R., Calsina, À., Cuadrado, S. et al. Delay equation formulation of a cyclin-structured cell population model. J. Evol. Equ. 14, 841–862 (2014). https://doi.org/10.1007/s00028-014-0241-7

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  • DOI: https://doi.org/10.1007/s00028-014-0241-7

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