A Logical Characterization of Individual-Based Models

Individual-based models are a relatively new approach to modelling dynamical systems of interacting entities, for example molecules in a biological cell. Although they are computationally expensive, they have the capability of modelling systems more realistically than traditional state-variable models. We give a formal definition of individual-based models, which includes state-variable models as a special case. We examine the questions of when state-variable models are sufficient for accurate modelling of a system, and when individual-based models are necessary. We define notions of abstraction and approximation, and give sufficient conditions that imply that an individual-based model can be approximated by a deterministic state-variable model. We also give negative results: examples of individual-based models that cannot be approximated by any state-variable model.