Identification of a branching process model for adaptive immune response

T-cell primary activation is a key event in the initiation of the adaptive immune response. Quantifying T-cell proliferation is extremely important to understand essential features of the immune response to vaccine or infection stimulus. Although mathematical models represent an attractive tool for analysis, they have been used almost exclusively for studying in vitro experiments. In this paper, we adopt a multi-type branching process with immigration to model T-cell proliferation in in vivo experiments. A maximum likelihood approach has been used to estimate model parameters, using T-cell relative frequencies instead of cell counts. Parameter estimates which represent the probabilities of division and death of the different cell generations, provide meaningful information on T-cell population kinetics.