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

The aim of this paper is to carry out a mathematical analysis of a system of ordinary differential equations introduced by R. 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.