Probabilistic cellular automaton describing a biological immune system

We have analyzed a probabilistic cellular automaton to describe the $T$-helper cells response under parasitic infections. The evolution rules are of totalistic type and possess "up-down" symmetry. The automaton displays a dynamical phase transition, from a disordered state to an ordered one, which takes place through a spontaneous symmetry breaking. In the ordered phase, one type of $T$-helper cells predominates over the others. The phase transition was studied both by a pair approximation and by Monte Carlo simulations. In addition, we were able to obtain some exact results for the densities of $T$-helper cells.