Abstract
In 1760 Daniel Bernoulli wrote an article modeling smallpox. In his time there was much controversy around inoculation, a practice that could protect people but could also be deadly. He used Halley’s life table and some data concerning smallpox to show that inoculation was advantageous if the associated risk of dying was less than 11%. Inoculation could increase life expectancy at birth up to three years. D’Alembert criticized Bernoulli’s work, which was the first mathematical model in epidemiology.
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Further reading
d’Alembert, J.: Onzième mémoire, Sur l’application du calcul des probabilités à l’inoculation de la petite vérole. In: Opuscules mathématiques, Tome second, pp. 26–95. David, Paris (1761). books.google.com
Bernoulli, D.: Réflexions sur les avantages de l’inoculation. Mercure de France, 173–190 (1760). Also in: Die Werke von Daniel Bernoulli, Band 2, pp. 268–274. Birkhäuser, Basel (1982). books.google.com
Bernoulli, D.: Essai d’une nouvelle analyse de la mortalité causée par la petite vérole et des avantages de l’inoculation pour la prévenir. Hist. Acad. R. Sci. Paris, 1–45 (1760/1766). English translation: Rev. Med. Virol. 14, 275–288 (2004). gallica.bnf.fr
Dietz, K., Heesterbeek, J.A.P.: Daniel Bernoulli’s epidemiological model revisited. Math. Biosci. 180, 1–21 (2002)
Duvillard, E.E.: Analyse et tableaux de l’influence de la petite vérole sur la mortalité à chaque âge. Imprimerie Impériale, Paris (1806). books.google.com
Lambert, J.H.: Contributions mathématiques à l’étude de la mortalité et de la nuptialité (1765 et 1772). INED, Paris (2006). books.google.com
Laplace, P.S.: Théorie analytique des probabilités. Courcier, Paris (1812). books.google.com
Straub, H.: Bernoulli, Daniel. In: Gillespie, C.C. (ed.) Dictionary of Scientific Biography, vol. 2, pp. 36–46. Scribner, New York (1970)
Tent, M.B.W.: Leonhard Euler and the Bernoullis. A K Peters, Natick, Massachusetts (2009)
Voltaire: Lettres philosophiques. Lucas, Amsterdam (1734). gallica.bnf.fr
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© 2011 Springer-Verlag London Limited
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Bacaër, N. (2011). Daniel Bernoulli, d’Alembert and the inoculation of smallpox (1760). In: A Short History of Mathematical Population Dynamics. Springer, London. https://doi.org/10.1007/978-0-85729-115-8_4
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DOI: https://doi.org/10.1007/978-0-85729-115-8_4
Publisher Name: Springer, London
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