Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 115, pp. 1-10.

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

Author: Alan D. Rendall (Max-Planck-Institut, Potsdam, Germany)

Abstract:
 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.