Abstract
In 1838 the Belgian mathematician Verhulst introduced the logistic equation, which is a kind of generalization of the equation for exponential growth but with a maximum value for the population. He used data from several countries, in particular Belgium, to estimate the unknown parameters. The work of Verhulst was rediscovered only in the 1920s.
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Further reading
Lloyd, P.J.: American, German and British antecedents to Pearl and Reed’s logistic curve. Pop. Stud. 21, 99–108 (1967)
McKendrick, A.G., Kesava Pai, M.: The rate of multiplication of micro-organisms: A mathematical study. Proc. R. Soc. Edinb. 31, 649–655 (1911)
Pearl, R.: The Biology of Death. Lippincott, Philadelphia (1922). www.archive.org
Pearl, R., Reed, L.J.: On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proc. Natl. Acad. Sci. 6, 275–288 (1920). www.pnas.org
Quetelet, A.: Sur l’homme et le développement de ses facultés. Bachelier, Paris (1835). gallica.bnf.fr
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Quetelet, A.: Sciences mathématiques et physiques au commencement du xix ième siècle. Mucquardt, Bruxelles (1867). gallica.bnf.fr
Robertson, T.B.: On the normal rate of growth of an individual and its biochemical significance. Arch. Entwicklungsmechanik Org. 25, 581–614 (1908)
Verhulst, P.-F.: Notice sur la loi que la population poursuit dans son accroissement. Corresp. Math. Phys. 10, 113–121 (1838). books.google.com
Verhulst, P.-F.: Recherches mathématiques sur la loi d’accroissement de la population. Nouv. Mém. Acad. R. Sci. B.-lett. Brux. 18, 1–45 (1845). gdz.sub.uni-goettingen.de
Verhulst, P.-F.: Deuxième mémoire sur la loi d’accroissement de la population. Mém. Acad. R. Sci. Lett. B.-Arts Belg. 20, 142–173 (1847). www.digizeit-schriften.de
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Bacaër, N. (2011). Verhulst and the logistic equation (1838). In: A Short History of Mathematical Population Dynamics. Springer, London. https://doi.org/10.1007/978-0-85729-115-8_6
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DOI: https://doi.org/10.1007/978-0-85729-115-8_6
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