Smallpox and the double decrement table: a piece of actuarial prehistory

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Abstract
More than 200 years ago, on 30 April 1760, Daniel Bernoulli (1766) read a memoir to the Royal Academy of Sciences in Paris entitled Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir (see Bradley, 1971, for a translation). In this remarkable memoir Bernoulli produced the first double decrement life table and one of the related single decrement tables, as well as deriving a mathematical model of the behaviour of smallpox in a community. This model was the forerunner of considerable developments in the mathematical theory of infectious diseases, a description of which is given in N. T. J. Bailey (1975). During the half century following Bernoulli's memoir there were a number of papers by other authors on the subject of that memoir; these, and the original memoir, seem to be little known to actuaries and are the subject of the present paper. They could have been the starting point of the actuarial development of exposed-to-risk formulae, but in fact were not.