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On interarrival times in simple stochastic epidemic models

Published online by Cambridge University Press:  14 July 2016

Grace Yang  and
C. L. Chiang
Grace Yang*
Affiliation:
University of Maryland, College Park
C. L. Chiang*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.
∗∗ Postal address: Department of Biomedical and Environmental Sciences, School of Public Health, University of California, Berkeley, CA 94720, U.S.A.
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Abstract

The probability distributions of the size and the duration of simple stochastic epidemic models are well known. However, in most instances, the solutions are too complicated to be of practical use. In this note, interarrival times of the infectives are utilized to study asymptotic distributions of the duration of the epidemic for a class of simple epidemic models. A brief summary of the results on simple epidemic models in terms of interarrival times is included.

Keywords

ASYMPTOTIC DISTRIBUTIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 4 , December 1982 , pp. 835 - 841
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research supported in part by USDA under contract no. 53–32U4–1–208.

References

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics, 1st edn. Griffin, London.Google Scholar
Bailey, N. T. J. (1963) The simple stochastic epidemic: a complete solution in terms of known functions. Biometrika 50, 235–240.CrossRefGoogle Scholar
Bailey, N. T. J. (1975) The Mathematical Theory of Infectious Diseases, 2nd edn. Hafner, New York.Google Scholar
Bartlett, M. S. (1949) Some evolutionary stochastic processes. J. R. Statist. Soc. B 11, 211–229.Google Scholar
Billard, L., Lacayo, H. and Langberg, N. A. (1979) A new look at the simple epidemic process. J. Appl. Prob. 16, 198–202.CrossRefGoogle Scholar
Dietz, K. (1967) Epidemics and rumors: a survey. J. R. Statist. Soc. A 130, 505–528.Google Scholar
Haskey, H. W. (1954) A general expression for the mean in a simple stochastic epidemic. Biometrika 41, 272–275.Google Scholar
Kendall, D. G. (1957) La propagation d'une épidémie ou d'un bruit dans une population limitée. Publ. Inst. Statist. Univ. Paris 6, 307–311.Google Scholar
Loeve, M. (1960) Probability Theory, 2nd edn. Van Nostrand.Google Scholar
Mansfield, E. and Hensley, C. (1960) The logistic process: tables of the stochastic epidemic curve and applications. J. R. Statist. Soc. B 22, 322–327.Google Scholar
Severo, N. C. (1969a) Generalizations of some stochastic epidemic models. Math. Biosci. 4, 395–402.CrossRefGoogle Scholar
Yang, G. (1972) On the probability distribution of some stochastic epidemic models. Theoret. Popn Biol. 3, 448–459.CrossRefGoogle ScholarPubMed
Yang, G. and Chiang, C. L. (1971) A time-dependent simple stochastic epidemic. Proc. 6th Berkeley Symp. Math. Statist. Prob. 6, 147–158.Google Scholar