[Preprint of chapter 2 of Epidemic Models: their Structure and Relation to Data, ed. Denis Mollison, Cambridge UP 1995.] The Structure of Epidemic Models

This paper reviews the basic components of epidemic models, and discusses some of the different ways of combining them, and relations between the re-sulting models. The fundamental aim is to help understanding of the relation between assumptions and the resulting dynamics: because without such un-derstanding even a model which fits data perfectly can be of no scientific value. Analysis of the structure of epidemic models is vital because of (1) the scarcity of good data and (2) the sensitive dependence of results on assump-tions. In evaluating model dynamics, we need to look carefully at their de-pendence, not only on parameters, but also on the structure of the model: for instance, whether the population is treated as stochastic or deterministic, dis-crete or continuous, and how the timing and distribution of infectious contacts within the population is modelled. The practical target is to identify those parts of models that have most effect on dynamics: a few key parameters can drive a model (see e.g. Mollison 1984, 1985, Cairns, this volume)