On a Model of Leukemia Development with a Spatial Cell Distribution
Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 101-120
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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.
@article{10_1051_mmnp:2007005,
author = {A. Ducrot and V. Volpert},
title = {On a {Model} of {Leukemia} {Development} with a {Spatial} {Cell} {Distribution}},
journal = {Mathematical modelling of natural phenomena},
pages = {101--120},
publisher = {mathdoc},
volume = {2},
number = {3},
year = {2007},
doi = {10.1051/mmnp:2007005},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007005/}
}
TY - JOUR AU - A. Ducrot AU - V. Volpert TI - On a Model of Leukemia Development with a Spatial Cell Distribution JO - Mathematical modelling of natural phenomena PY - 2007 SP - 101 EP - 120 VL - 2 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007005/ DO - 10.1051/mmnp:2007005 LA - en ID - 10_1051_mmnp:2007005 ER -
%0 Journal Article %A A. Ducrot %A V. Volpert %T On a Model of Leukemia Development with a Spatial Cell Distribution %J Mathematical modelling of natural phenomena %D 2007 %P 101-120 %V 2 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2007005/ %R 10.1051/mmnp:2007005 %G en %F 10_1051_mmnp:2007005
A. Ducrot; V. Volpert. On a Model of Leukemia Development with a Spatial Cell Distribution. Mathematical modelling of natural phenomena, Tome 2 (2007) no. 3, pp. 101-120. doi: 10.1051/mmnp:2007005
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