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Biometrika 1972 59(2):455-461; doi:10.1093/biomet/59.2.455
© 1972 by Biometrika Trust
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On Downton's carrier-borne epidemic

GILLIAN M. DENTON

University of Sheffield

The stochastic version of Downton's (1968) carrier-borne epidemic is considered. From the time-dependent solution, obtained by Gani's (1967) technique, the distribution of the total size of the continuous time epidemic is found, in a form suitable for computer calculations. Two additional results obtained seem useful and practical. An (n + 1) x (n + 1) matrix with first column the distribution of the size of an epidemic initiated by n susceptibles and a. carriers is shown to give the distributions of epidemics initiated by 0, ..., n – 1 susceptibles and a carriers; this matrix is also shown to be the {alpha}-fold product of a similar matrix for epidemics initiated by just one carrier. The first of the additional results has an analogue for the time-dependent solution.

Key Words: Carrier-borne epidemic • Time-dependent distribution of the size of epidemic • Distribution of total size of epidemic


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