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On the model of Weiss for the spread of epidemics by carriers

Published online by Cambridge University Press:  14 July 2016

Klaus Dietz
Klaus Dietz*
Affiliation:
Institut für medizinische Statistik und Dokumentation, Freiburg
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Extract

1. Recently Weiss [7] constructed a stochastic model for the spread of diseases e.g. typhoid, by carriers. He assumed that a carrier is eliminated in (t, t + dt) with probability βrdt, where r is the number of carriers extant at time t and that a susceptible is infected in (t, t + dt) with probability arsdt where s is the number of susceptibles at time t. Thus only the carriers are responsible for the spread of the disease.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 2 , December 1966 , pp. 375 - 382
Copyright
Copyright © Applied Probability Trust 

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References

[1] Adams, E. P. (1947) Smithsonian Mathematical Formulae. City of Washington.Google Scholar
[2] Bailey, N. T. J. (1964) The Elements of Stochastic Processes, John Wiley, New York.Google Scholar
[3] Erdelyi, A., (Ed.) (1954) Tables of Integral Transforms, Vol. I. McGraw-Hill, New York.Google Scholar
[4] Gani, J. (1965) On the general stochastic epidemic. Fifth Berkeley Symp. Math. Statist. Prob. (to appear).Google Scholar
[5] Jordan, C. (1950) Calculus of Finite Differences. Chelsea, New York.Google Scholar
[6] Netto, E. (1927) Lehrbuch der Combinatorik. Chelsea, New York.Google Scholar
[7] Weiss, G. H. (1965) On the spread of epidemics by carriers. Biometrics, 21, 481–490.Google Scholar