(a) A mathematical function with parameters that can be adjusted so the function closely describes a set of empirical data. A mechanistic model usually reflects observed or hypothesized biological or physical mechanisms, and has model parameters with real world interpretation. In contrast, statistical or empirical models selected for particular numerical properties are fitted to data; model parameters may or may not have real world interpretation. When data quality is otherwise equivalent, extrapolation from mechanistic models (e.g., biologically based dose_response models) often carries higher confidence than extrapolation using empirical models (e.g., logistic model). [IRIS, 1999: Glossary of IRIS Terms]; (b) A representation or simulation of an actual situation. This may be either (1) a mathematical representation of characteristics of a situation that can be used to examine consequences of various actions, or (2) a representation of a country's situation through an "average region" with characteristics resembling those of the whole country. In epidemiology the use of models began with an effort to predict the onset and course of epidemics. In the second report of the Registrar_General of England and Wales (1840), William Farr developed the beginnings of a predictive model for communicable disease epidemics. He had recognized regularities in the smallpox epidemics of the 1830s. By calculating frequency curves for these past outbreaks, he estimated the deaths to be expected. [Last, 1983: A Dictionary of Epidemiology]; (c) A mathematical representation of a natural system intended to mimic the behavior of the real system, allowing description of empirical data and predictions about untested states of the system. [USEPA, 1995: Benchmark Dose]