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Epidemics with carriers: A note on a paper of Dietz

Published online by Cambridge University Press:  14 July 2016

F. Downton
F. Downton*
Affiliation:
University of Birmingham
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Extract

In a recent paper Weiss (1965) has suggested a simple model for a carrier-borne epidemic such as typhoid. He considers a population (of size m) of susceptibles into which a number (k) of carriers is introduced. These carriers exhibit no overt symptoms and are only detectable by the discovery of infected persons. He supposed that after the initial introduction of the carriers, the population remains entirely closed and no new carriers arise. The epidemic then progresses until either all the carriers have been traced and isolated or until the entire population has succumbed to the disease.

Type
Research Papers
Information
Journal of Applied Probability , Volume 4 , Issue 2 , August 1967 , pp. 264 - 270
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Griffin, London.Google Scholar
Daniels, H. E. (1967) The distribution of the total size of an epidemic. Proc. Fifth Berkeley Symposium on Mathematical Statistics and Probability (to appear).Google Scholar
Davis, H. T. (1935) Tables of the Higher Mathematical Functions, Vol. 2. Principia Press, Bloomington, Indiana.Google Scholar
Dietz, K. (1966) On the model of Weiss for the spread of epidemics by carriers. J. Appl. Prob. 3, 375–382.CrossRefGoogle Scholar
Downton, F. (1967) A note on the ultimate size of a general stochastic epidemic. Biometrika (to appear).CrossRefGoogle Scholar
Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics 21, No. 2, 481–490.CrossRefGoogle ScholarPubMed