Delay equation formulation of a cyclin-structured cell population model

Ricardo Borges; Àngel Calsina; Sílvia Cuadrado; Odo Diekmann

doi:10.1007/s00028-014-0241-7

Delay equation formulation of a cyclin-structured cell population model

Ricardo Borges, Àngel Calsina, Sílvia Cuadrado, Odo Diekmann

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

Abstract

© 2014, Springer Basel. 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.

Original language	English
Pages (from-to)	841-862
Journal	Journal of Evolution Equations
Volume	14
Issue number	4-5
DOIs	https://doi.org/10.1007/s00028-014-0241-7
Publication status	Published - 1 Jan 2014

Keywords

45D05
47D06
92C37
92D25

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10.1007/s00028-014-0241-7

Cite this

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AU - Borges, Ricardo

AU - Calsina, Àngel

AU - Cuadrado, Sílvia

AU - Diekmann, Odo

PY - 2014/1/1

Y1 - 2014/1/1

N2 - © 2014, Springer Basel. 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.

AB - © 2014, Springer Basel. 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.

KW - 45D05

KW - 47D06

KW - 92C37

KW - 92D25

U2 - 10.1007/s00028-014-0241-7

DO - 10.1007/s00028-014-0241-7

M3 - Article

VL - 14

SP - 841

EP - 862

JO - Journal of Evolution Equations

JF - Journal of Evolution Equations

SN - 1424-3199

IS - 4-5

ER -

Delay equation formulation of a cyclin-structured cell population model

Abstract

Keywords

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