Optimal strategies in immunology

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Abstract
After a first encounter with most antigens, the immune system responds to subsequent encounters with a faster, more efficient and more strenuous antibody response. The memory of previous antigen contacts is carried by lymphocytes. Expanding on the model developed in Part I of this paper, we examine the optimal strategy available to the immune system for B memory cell production. We again find that the strategy should be of the bang-bang variety. The model we consider assumes that antigen triggers a subpopulation of B-lymphocytes. These triggered lymphocytes can proliferate and secrete modest amounts of antibody, differentiate into non-dividing plasma cells which secrete large amounts of antibody, or differentiate into non-antibody secreting memory cells. Given injections of antigen at two widely spaced times we compute the strategy which minimizes a linear combination of the primary and secondary response times. We find that for all biologically reasonable parameter values the best strategies are ones in which memory cells are produced at the end of the primary response. Experimental results which bear on the actual strategies employed are discussed.