# Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models

J. Clairambault; S. Gaubert; Th. Lepoutre

Mathematical Modelling of Natural Phenomena (2009)

- Volume: 4, Issue: 3, page 183-209
- ISSN: 0973-5348

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topClairambault, J., Gaubert, S., and Lepoutre, Th.. "Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models." Mathematical Modelling of Natural Phenomena 4.3 (2009): 183-209. <http://eudml.org/doc/222182>.

@article{Clairambault2009,

abstract = {
We study the growth rate of a cell population that follows an
age-structured PDE with time-periodic coefficients. Our motivation
comes from the comparison between experimental tumor growth curves
in mice endowed with intact or disrupted circadian clocks,
known to exert their influence on the cell division cycle.
We compare the growth rate of the model controlled by a time-periodic
control on its coefficients with the growth rate of stationary
models of the same nature, but with averaged coefficients.
We firstly derive a delay differential equation which allows us to prove
several inequalities and equalities on the growth rates. We also
discuss about the necessity to take into account the structure of
the cell division cycle for chronotherapy modeling. Numerical simulations
illustrate the results.
},

author = {Clairambault, J., Gaubert, S., Lepoutre, Th.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {cell cycle; circadian rhythms; chronotherapy; structured PDEs; delay
differential equations; time-periodic coefficients; time-periodic control; averaged coefficients},

language = {eng},

month = {6},

number = {3},

pages = {183-209},

publisher = {EDP Sciences},

title = {Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models},

url = {http://eudml.org/doc/222182},

volume = {4},

year = {2009},

}

TY - JOUR

AU - Clairambault, J.

AU - Gaubert, S.

AU - Lepoutre, Th.

TI - Comparison of Perron and Floquet Eigenvalues in Age Structured Cell Division Cycle Models

JO - Mathematical Modelling of Natural Phenomena

DA - 2009/6//

PB - EDP Sciences

VL - 4

IS - 3

SP - 183

EP - 209

AB -
We study the growth rate of a cell population that follows an
age-structured PDE with time-periodic coefficients. Our motivation
comes from the comparison between experimental tumor growth curves
in mice endowed with intact or disrupted circadian clocks,
known to exert their influence on the cell division cycle.
We compare the growth rate of the model controlled by a time-periodic
control on its coefficients with the growth rate of stationary
models of the same nature, but with averaged coefficients.
We firstly derive a delay differential equation which allows us to prove
several inequalities and equalities on the growth rates. We also
discuss about the necessity to take into account the structure of
the cell division cycle for chronotherapy modeling. Numerical simulations
illustrate the results.

LA - eng

KW - cell cycle; circadian rhythms; chronotherapy; structured PDEs; delay
differential equations; time-periodic coefficients; time-periodic control; averaged coefficients

UR - http://eudml.org/doc/222182

ER -

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