Electron. J. Diff. Equ., Vol. 2010(2010), No. 115, pp. 1-10.

Analysis of a mathematical model for interactions between T cells and macrophages

Alan D. Rendall

The aim of this article is to carry out a mathematical analysis of a system of ordinary differential equations introduced by Lev Bar-Or to model the interactions between T cells and macrophages. Under certain restrictions on the parameters of the model, theorems are proved about the number of stationary solutions and their stability. In some cases the existence of periodic solutions or heteroclinic cycles is ruled out. Evidence is presented that the same biological phenomena could be equally well described by a simpler model.

Submitted August 5, 2010. Published August 19, 2010.
Math Subject Classifications: 37N25, 92C37.
Key Words: Dynamical systems; qualitative behaviour; immunology.

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Alan D. Rendall
Max-Planck-Institut für Gravitationsphysik
Am Mühlenberg 1, 14476 Potsdam, Germany
email: rendall@aei.mpg.de

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