ABSTRACT
This chapter aims to apply the boolean approach to obtain a step-by-step mathematical procedure for developing an immune response model. The procedure is used to obtain a minimal two-lymphocyte model that simulates a set of nine immune response patterns. Various mathematical models have been introducted with an eye toward capturing salient aspects of immune response phenomena, suggesting new experiments, and perhaps most importantly. Classical experiments already testify to the enormous complexity involved in the immune response. Both Herzenberg et al. and Kaufman et al. introduced several minimal models of the immune response phenomena. The immune responses are initiated by introducing antigen at one of three possible levels when the system is in one of the three steady states, memory, tolerance or the virgin state. Antigen drives transitions between states by stimulating some yet-to-be-elucidated sequence of biochemical events that ultimately lead to shifts in the population balance by turning some cell types on, and turning others off.
