Abstract
In 1926 McKendrick studied a stochastic epidemic model and found a method to compute the probability for an epidemic to reach a certain final size. He also discovered the partial differential equation governing age-structured populations in a continuous-time framework. In 1927 Kermack and McKendrick studied a deterministic epidemic model and obtained an equation for the final epidemic size, which emphasizes a certain threshold for the population density. Large epidemics can occur above but not below this threshold. These works are still very much used in contemporary epidemiology.
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Further reading
Advisory Committee appointed by the Secretary of State for India, the Royal Society and the Lister Institute: Reports on plague investigations in India, XXII, Epidemiological observations in Bombay City. J. Hyg. 7, 724–798 (1907). www.ncbi.nlm.nih.gov
Davidson, J.N., Yates, F., McCrea, W.H.: William Ogilvy Kermack 1898–1970. Biog. Mem. Fellows R. Soc. 17, 399–429 (1971)
Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J.: On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28, 365–382 (1990)
Gani, J.: A.G. McKendrick. In: Heyde, C.C., Seneta, E. (eds.) Statisticians of the Centuries, pp. 323–327. Springer, New York (2001). books.google.com
Harvey, W.F.: A.G. McKendrick 1876–1943. Edinb. Med. J. 50, 500–506 (1943)
McKendrick, A.G.: Applications of mathematics to medical problems. Proc. Edinb. Math. Soc. 13, 98–130 (1926)
Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A 115, 700–721 (1927). gallica.bnf.fr
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Bacaër, N. (2011). McKendrick and Kermack on epidemic modelling (1926–1927). In: A Short History of Mathematical Population Dynamics. Springer, London. https://doi.org/10.1007/978-0-85729-115-8_16
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DOI: https://doi.org/10.1007/978-0-85729-115-8_16
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