Qualitative Methods in Immunological Modelling

The immune system is a complex system that learns, remembers what it has learned and acts to protect the organism against various diseases (antigens). Here we discuss simple mathematical concepts that can be used to model these features of the immune response in a quantitative way. We identify two design principles for immune system recognition. Using the concept of shape space we analyze the reaction of the immune system to invasion by a foreign antigen. This analysis leads to a distinction between specialist and generalist antibodies. We then consider the case of a mutating antigen which is "hunted" by the immune system. The relevant biology is explained in a highly simplified way, and the mathematical analysis is outlined in a global way.