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space cell distribution

Mathematical Modelling of Natural Phenomena (1)

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On a Model of Leukemia Development with a SpatialCell Distribution
A. Ducrot, V. Volpert
Journal:

Mathematical Modelling of Natural Phenomena / Volume 2 / Issue 3 / 2007

Published online by Cambridge University Press:

15 June 2008, pp. 101-120

Print publication:

2007
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In this paper we propose a mathematical model to describe the evolution of leukemiain the bone marrow. The model is based on a reaction-diffusion system of equations in a porousmedium. We show the existence of two stationary solutions, one of them corresponds to the normalcase and another one to the pathological case. The leukemic state appears as a result of a bifurcationwhen the normal state loses its stability. The critical conditions of leukemia developmentare determined by the proliferation rate of leukemic cells and by their capacity to diffuse. Theanalytical results are confirmed and illustrated by numerical simulations.