A local-field-type model for immunological systems: time evolution in real and shape spaces

We introduce a new model for the interaction of immunological cells that takes into account their location in real space. Each one of the model cells mimics the real B cells in the sense that they detect antigens and they are also capable of reproducing themselves. We perform computer simulations for the simplest cases. The main differences between the results obtained within this model and those obtained through the usual models, which do not consider a real space, concern the final stationary states. In mean field calculations not only the system as a whole but also each individual cell population reach an equilibrium state. In the present approach the entire system reaches a stationary state, but the individual populations present strong fluctuations, at least for the explored range of parameters. We exhibit that, in spite of the simplicity of the present model, interesting real-space effects can take place.