What Is a Good Model?

Mathematical models are simplified representations of reality, including only a subset of features or behaviors that are of interest. This paper reviews the most distinguishing properties of good models and of correct system design, with a focus on models describing the functioning of a system in terms of subcomponents and relationships (mechanistic models). Ingredients of good models include usefulness, mathematical coherence, statistical robustness, meaningfulness and interpretability, generalization capabilility, parsimony, tractability, falsifiability. Deterministic and stochastic mathematical models are now of widespread use for different goals: analysis or interpretation of the past, prediction of future behavior, numerical simulation, diagnosis of dangerous/critical events, control and decision making. Within the many modern applications of mathematical models, we highlight their increasing role in biology and medicine, and we support our discussion with examples from endocrinology.