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Displaying similar documents to “Stability analysis of a model of atherogenesis: an energy estimate approach. II.”

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...

Immunological barrier for infectious diseases

I. Barradas (1997)

Applicationes Mathematicae

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A nonlinear mathematical model with distributed delay is proposed to describe the reaction of a human organism to a pathogen agent. The stability of the disease free state is analyzed, showing that there exists a large set of initial conditions in the attraction basin of the disease-free state whose border is defined as the immunological barrier.

Dynamics of the tumor-immune system competition - the effect of time delay

Magda Galach (2003)

International Journal of Applied Mathematics and Computer Science

Similarity:

The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order...