Optimal Control of a Cancer Cell Model with Delay

C. Collins; K.R. Fister; M. Williams

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 3, page 63-75
  • ISSN: 0973-5348

Abstract

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In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are discussed.

How to cite

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Collins, C., Fister, K.R., and Williams, M.. "Optimal Control of a Cancer Cell Model with Delay." Mathematical Modelling of Natural Phenomena 5.3 (2010): 63-75. <http://eudml.org/doc/197660>.

@article{Collins2010,
abstract = {In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are discussed.},
author = {Collins, C., Fister, K.R., Williams, M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {cancer dynamics; optimal control},
language = {eng},
month = {4},
number = {3},
pages = {63-75},
publisher = {EDP Sciences},
title = {Optimal Control of a Cancer Cell Model with Delay},
url = {http://eudml.org/doc/197660},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Collins, C.
AU - Fister, K.R.
AU - Williams, M.
TI - Optimal Control of a Cancer Cell Model with Delay
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/4//
PB - EDP Sciences
VL - 5
IS - 3
SP - 63
EP - 75
AB - In this paper, we look at a model depicting the relationship of cancer cells in different development stages with immune cells and a cell cycle specific chemotherapy drug. The model includes a constant delay in the mitotic phase. By applying optimal control theory, we seek to minimize the cost associated with the chemotherapy drug and to minimize the number of tumor cells. Global existence of a solution has been shown for this model and existence of an optimal control has also been proven. Optimality conditions and characterization of the control are discussed.
LA - eng
KW - cancer dynamics; optimal control
UR - http://eudml.org/doc/197660
ER -

References

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