McKendrick and Kermack on epidemic modelling (1926–1927)

  • Nicolas Bacaër


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.


Epidemic Modelling Infected Person Infected People Secondary Case Epidemic Size 
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Further reading

  1. 1.
    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). Google Scholar
  2. 2.
    Davidson, J.N., Yates, F., McCrea, W.H.: William Ogilvy Kermack 1898–1970. Biog. Mem. Fellows R. Soc. 17, 399–429 (1971) CrossRefGoogle Scholar
  3. 3.
    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) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gani, J.: A.G. McKendrick. In: Heyde, C.C., Seneta, E. (eds.) Statisticians of the Centuries, pp. 323–327. Springer, New York (2001). Google Scholar
  5. 5.
    Harvey, W.F.: A.G. McKendrick 1876–1943. Edinb. Med. J. 50, 500–506 (1943) Google Scholar
  6. 6.
    McKendrick, A.G.: Applications of mathematics to medical problems. Proc. Edinb. Math. Soc. 13, 98–130 (1926) Google Scholar
  7. 7.
    Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A 115, 700–721 (1927). CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.IRD (Institut de Recherche pour le Développement)BondyFrance

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