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Maximum-likelihood estimation of the relative removal rate from the distribution of the total size of an intra-household epidemic

Published online by Cambridge University Press:  15 May 2009

Norman T. J. Bailey
Affiliation:
Nuffield Lodge, Regent's Park, London
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Extract

In a previous paper (Bailey, 1953a) I discussed the distribution of the total size of a stochastic epidemic, involving both infection and removal, in a given group of homogeneously mixing susceptibles. The model employed was of the ‘continuous infection’ type, according to which infected individuals continue as sources of infection until removed from circulation by recovery, death or isolation. This may be contrasted with the chain-binomial type of model which entails short periods of high infectivity and approximately constant incubation periods (see, for example, Greenwood, 1931, 1949; Lidwell & Sommerville, 1951; Bailey, 1953b). The basic assumptions are that, with x susceptibles and y infectious persons in circulation, the chance of one new infection taking place in time dt is βxy dt, while the chance of a removal is γy dt, where β and γ are the infection and removal rates, respectively.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1954

References

Bailey, N. T. J. (1953 a). The total size of a general stochastic epidemic. Biometrika, 40, 177.CrossRefGoogle Scholar
Bailey, N. T. J. (1953 b). The use of chain-binomials with a variable chance of infection for the analysis of intra-household epidemics. Biometrika, 40, 279.CrossRefGoogle Scholar
Fisher, R. A. & Yates, F. (1948). Statistical Tables (3rd. ed.). London: Oliver and Boyd.Google Scholar
Greenwood, M. (1931). On the statistical measure of infectiousness. J. Hyg., Camb., 31, 336.CrossRefGoogle ScholarPubMed
Greenwood, M. (1949). The infectiousness of measles. Biometrika, 36, 1.CrossRefGoogle Scholar
Lidwell, O. M. & Sommerville, T. (1951). Observations on the incidence and distribution of the common cold in a rural community during 1948 and 1949. J. Hyg., Camb., 49, 365.CrossRefGoogle Scholar
Wilson, E. B., Bennett, C., Allen, M. & Worcester, J. (1939). Measles and scarlet fever in Providence, R.I., 1929–34 with respect to age and size of family. Proc. Amer. phil. Soc. 80, 357.Google Scholar
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Maximum-likelihood estimation of the relative removal rate from the distribution of the total size of an intra-household epidemic
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