Predicting the impact of infectious diseases on the well-being of the community is a cornerstone of identifying effective prevention, control and support. One only has to reflect on the last few years in the United Kingdom to see the impact mathematical modelling has had on public and government, with controversy around the likely numbers of sufferers from new-variant Creutzfeld–Jakob disease, human immunodeficiency virus, and continuing debate as to whether to use vaccine to support control of foot-and-mouth disease. Over the last 20–25 years, Epidemiology and Infection, and before it the Journal of Hygiene, have published many of the sentinel papers in the mathematical modelling of infectious disease, both in humans and animals. The discipline has advanced from relatively simple analyses to the most complex assessments whose underlying mathematics and statistics almost certainly exceed the comprehension of all but a few microbiologists and public health specialists. The depth of the analysis does not obscure the key messages, however, for the epidemiology of infectious disease and its control, and a Special Article in the journal in 1988 overviewed its contribution [1].