A dilute bootstrap percolation: Lattice model for unresponsiveness in T-cell immunology

Abstract

The biased majority rule of cellular automata takes a spin up if and only if at least two of its four nearest neighbors on the square lattice are up. We generalize this type of bootstrap percolation by introducing quenched site dilution as well as a random birth and decay process. Our Monte Carlo simulations then give first-order transitions qualitatively similar to our results from meanfield reaction equations describing the induction of T-cell unresponsiveness in the immune system.