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The aim of this paper is to prove results about the existence and stabilityof multiple steady states in a system of ordinary differential equationsintroduced by R. Lev Bar-Or to model the interactions between T cells andmacrophages. Previous results showed that for certain values of the parametersthese equations have three stationary solutions, two of which are stable. Hereit is shown that there are values of the parameters for which the number ofstationary solutions is at least seven and the number of stable stationarysolutions at least four. This requires approaches different to those used inexisting work on this subject. In addition, a rather explicit characterizationis obtained of regions of parameter space for which the system has a givennumber of stationary solutions.

Multiple steady states in a mathematical model for interactions between T cells and macrophages