  In this paper we consider a model based on branching process theory for the
proliferation and the dissemination network of T cells in the adaptive immune
response. A multi-type Galton Watson branching process is assumed as the basic
proliferation mechanism, associated to the migration of T cells of the
different generations from the draining lymph node to the spleen and other
lymphoid organs. Time recursion equations for the mean values and the
covariance matrices of the the cell population counts are derived in all the
compartments of the network model. Moreover, a normal approximation of the
log-likelihood function of the cell relative frequencies is derived, which
allows one to obtain estimates of both the probability parameters of the
branching process and the migration rates in the various compartments of the
network.
