On a Model of Leukemia Development with a Spatial Cell Distribution

A. Ducrot; V. Volpert

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 2, Issue: 3, page 101-120
  • ISSN: 0973-5348

Abstract

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In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by the proliferation rate of leukemic cells and by their capacity to diffuse. The analytical results are confirmed and illustrated by numerical simulations.

How to cite

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Ducrot, A., and Volpert, V.. "On a Model of Leukemia Development with a Spatial Cell Distribution." Mathematical Modelling of Natural Phenomena 2.3 (2010): 101-120. <http://eudml.org/doc/222408>.

@article{Ducrot2010,
abstract = { In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by the proliferation rate of leukemic cells and by their capacity to diffuse. The analytical results are confirmed and illustrated by numerical simulations.},
author = {Ducrot, A., Volpert, V.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {leukemia; bone marrow; space cell distribution; reaction-diffusion system; porous medium},
language = {eng},
month = {3},
number = {3},
pages = {101-120},
publisher = {EDP Sciences},
title = {On a Model of Leukemia Development with a Spatial Cell Distribution},
url = {http://eudml.org/doc/222408},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Ducrot, A.
AU - Volpert, V.
TI - On a Model of Leukemia Development with a Spatial Cell Distribution
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 2
IS - 3
SP - 101
EP - 120
AB - In this paper we propose a mathematical model to describe the evolution of leukemia in the bone marrow. The model is based on a reaction-diffusion system of equations in a porous medium. We show the existence of two stationary solutions, one of them corresponds to the normal case and another one to the pathological case. The leukemic state appears as a result of a bifurcation when the normal state loses its stability. The critical conditions of leukemia development are determined by the proliferation rate of leukemic cells and by their capacity to diffuse. The analytical results are confirmed and illustrated by numerical simulations.
LA - eng
KW - leukemia; bone marrow; space cell distribution; reaction-diffusion system; porous medium
UR - http://eudml.org/doc/222408
ER -

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