Displaying similar documents to “Dynamics of Erythroid Progenitors and Erythroleukemia”

Influence of diffusion on interactions between malignant gliomas and immune system

Urszula Foryś (2010)

Applicationes Mathematicae

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We analyse the influence of diffusion and space distribution of cells in a simple model of interactions between an activated immune system and malignant gliomas, among which the most aggressive one is GBM Glioblastoma Multiforme. It turns out that diffusion cannot affect stability of spatially homogeneous steady states. This suggests that there are two possible outcomes-the solution is either attracted by the positive steady state or by the semitrivial one. The semitrivial steady state...

On a Model of Leukemia Development with a Spatial Cell Distribution

A. Ducrot, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

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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...

On Chemotaxis Models with Cell Population Interactions

Z. A. Wang (2010)

Mathematical Modelling of Natural Phenomena

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This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are...