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Delay equation formulation of a cyclin-structured cell population model

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Publication date

2014-12

Authors

Borges, Ricardo
Calsina, Angel
Cuadrado, Silvia
Diekmann, O.ORCID 0000-0003-4695-7601ISNI 0000000108765903

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DOI

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

Document Type

Article

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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.

Keywords

45D05, 47D06, 92D25, 92C37, Delay equations, Structured cell population, Initial value problem, Steady states, Linearized stability principle

Citation

Borges, R, Calsina, A, Cuadrado, S & Diekmann, O 2014, 'Delay equation formulation of a cyclin-structured cell population model', Journal of Evolution Equations, vol. 14, no. 4-5, pp. 841-862. https://doi.org/10.1007/s00028-014-0241-7

URI

https://dspace.library.uu.nl/handle/1874/306782