An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it. 1766.

INTRODUCTION Should the general population be vaccinated against smallpox (Variola Major)? Would the benefits of mass vaccination outweigh the risks? How many deaths would occur as the result of a mass vaccination campaign against smallpox? Can mathematical models of smallpox vaccination be used to determine health policy? Although smallpox was declared eradicated by the World Health Organization in 1979, these questions have all been recently debated based upon the premise that smallpox may be used as a weapon of bioterrorism. Hence, a series of analyses has recently been published that use mathematical models to try to determine the most effective public health response in the event of such an attack [1–4]. However, these same controversial public health questions were debated in the 18th century when smallpox was endemic and Reviews in Medical Virology has published two classic papers describing the natural history of smallpox in 1902 and 1913 to help inform these discussions [5,6]. We now publish an even earlier paper. In 1760 Daniel Bernoulli (1700–1782), one of the greatest scientists of the 18th century, wrote a mathematical analysis of the problem in order to try to influence public health policy by encouraging the universal inoculation against smallpox; his analysis was first presented at the Royal Academy of Sciences in Paris in 1760 and later published in 1766 [7]. Here, we republish and discuss both the historical and the current significance of Bernoulli’s classic paper. A detailed discussion of the mathematics of Bernoulli’s analysis has previously been presented by Dietz and Heesterbeck [8]. According to Creighton [9] smallpox first appeared in England in the 16th century. Smallpox was known in Western Europe in medieval times, but a particularly virulent strain emerged in the early 17th century and gradually the case fatality rate increased [10]. By the 18th century smallpox was endemic. Bernoulli calculated that approximately three quarters of all living people (in the 18th century) had been infected with smallpox [7]. One-tenth of all mortality at that time was due to smallpox, although there was considerable annual variation in smallpox mortality due to epidemic outbreaks overlaying the endemic smallpox mortality rate. For example, in London during the period 1761–1796 the annual number of deaths due to smallpox varied from 3000 to 15 000. Where smallpox was endemic it was almost wholly a disease of childhood, with a case-fatality rate of 20%– 30%; the mean age of death due to smallpox has been estimated as 2.6 years [10] or 4.5 years [11]. C L A S S I C