Stochastic approximation to the T cell mediated specific response of the immune system

We develop a stochastic model to study the specific response of the immune system. The model is based on the dynamical interaction between Regulatory and Effector CD4+ T cells in the presence of Antigen Presenting Cells inside a lymphatic node. At a mean field level the model predicts the existence of different regimes where active, tolerant, or cyclic immune responses are possible. To study the model beyond mean field and to understand the specific responses of the immune system we use the Linear Noise Approximation and show that fluctuations due to finite size effects may strongly alter the mean field scenario. Moreover, it was found that the existence of a certain characteristic frequency for the fluctuations. All the analytical predictions were compared with simulations using Gillespie's algorithm.