ABSTRACT
This chapter aims to apply methods of numerical bifurcation theory in the construction and evaluation of mathematical models of the immune response. It focuses on the dynamics of the interaction of T cells with IL-1, IL-2 and antigen at several levels of modeling complexity. The chapter examines the dependence of the qualitative dynamics on key parameters, and draws analogies between numerically predicted and experimentally observed behavior. It aims to concentrate on developing a model of T cell activation and proliferation in relation to the lymphokines involved in controlling the response. One of the more interesting features of IL-2 regulation of T cell growth is the fact that IL-2 is produced by activated T cells. The chapter concludes by discussing directions for future research, both in terms of modification of the existing models, and in terms of coupling several models of this type in an attempt to model a response to an antigen, containing multiple epitopes.
