A branching network model for T cell dissemination in adaptive immune response

TL;DR

This paper develops a mathematical branching process model to describe T cell proliferation and migration during the adaptive immune response, providing tools for parameter estimation and understanding immune dynamics.

Contribution

It introduces a multi-type Galton-Watson branching process model for T cell proliferation and migration, with derived equations for population statistics and likelihood-based parameter estimation.

Findings

Derived time recursion equations for mean and covariance of T cell populations.

Developed a normal approximation for the likelihood function of cell frequencies.

Provided methods for estimating proliferation and migration parameters.

Abstract

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.