ABSTRACT
A simple building-block synthesis of the immune system is presented. It is shown that, mathematically, this complex system consists of numerous cascades of bilinear processes which are themselves coupled together by nonlinear gain elements. The mathematical structure is further divided for convenience into cellular and molecular components with mainly molecular terms affecting nonlinear coupling. Interest in mathematical immunology has been growing. The mathematical study of events that are involved at the cellular level in transmission of information seems to be generally missing in the literature, the reference here being to the study of recirculation of lymphocytes. Cellular and molecular kinetics are the basis of the entire immune process. The immune system is a communication command and control system to defend the body from alien intrusion and infection. Compartmental models are presented, and, after modeling experimental data for lymphocyte circulation in rats, a discrete, stochastic bilinear, time-series approximation is statistically analyzed.
