The immune system recognizes a myriad of invading pathogens and their toxic
products. It does so with a finite repertoire of antibodies and T cell
receptors. We here describe theories that quantify the immune system dynamics.
We describe how the immune system recognizes antigens by searching the large
space of receptor molecules. We consider in some detail the theories that
quantify the immune response to influenza and dengue fever. We review
theoretical descriptions of the complementary evolution of pathogens that
occurs in response to immune system pressure. Methods including bioinformatics,
molecular simulation, random energy models, and quantum field theory contribute
to a theoretical understanding of aspects of immunity.Comment: 49 pages, 12 figures, to appear in Annual Review