Abstract

During an adaptive immune response, lymphocytes proliferate for ve to twenty cell divisions, then stop and die over a period of weeks. The cyton model for regulation of lymphocyte proliferation and survival was introduced by Hawkins et al. [17] to provide a framework for understanding this response and its regulation. The model assumes stochastic values for division and survival times for each cell in a responding population. Experimental evidence indicates that the choice of times is drawn from a skewed distribution such as the lognormal, with the fate of individual cells being potentially highly variable. For this reason we calculate the higher moments of the model so that the expected variability can be determined. To do this we formulate a new analytic framework for the cyton model by introducing a generalization to the Bellman-Harris branching process.