High-dimensional Simulation of Simple Immunological Models

We propose a simple model for idiotypic-antiidiotypic immunological networks which represents a simplification of the model originally suggested by Stewart & Varela, and de Boer, van der Laan & Hogeweg. Window cellular automata enlarge the antibody concentration if the influence of the immediate neighborhood lies between 70 and 99% of its maximum value; in addition random recruitment is possible. We simulate the model on large square lattices as well as in higher dimensions. The results are in qualitative agreement with those of the earlier model. Moreover, in five to ten dimensions we find phase separation for not too large recruitment, which then leads to domains growing to "infinity" for infinite times.