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The discrete asymptotic behaviour of a simple batch epidemic process

Published online by Cambridge University Press:  14 July 2016

L. Billard ,
H. Lacayo  and
N. A. Langberg
L. Billard*
Affiliation:
Florida State University
H. Lacayo*
Affiliation:
Florida State University
N. A. Langberg*
Affiliation:
Florida State University
*
∗Postal address for all authors: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, Florida 32306, U.S.A.
∗Postal address for all authors: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, Florida 32306, U.S.A.
∗Postal address for all authors: Department of Statistics and Statistical Consulting Center, The Florida State University, Tallahassee, Florida 32306, U.S.A.
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Abstract

A simple epidemic process in which the number of individuals who can become infected at any point in time is itself a random variable is described. The discrete asymptotic behaviour of such a process is discussed. In particular, the associated marginal distribution of the limiting process is considered.

Keywords

SIMPLE BATCH EPIDEMIC PROCESSLIMITING DISTRIBUTIONSMARGINAL DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 1 , March 1980 , pp. 25 - 32
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

†

Research supported by National Institutes of Health Grant No. 1 R01 GM26851–01.

‡

Research supported by Air Force Office of Scientific Research AFSC, USAF, under Grant AFOSR 74–2581D.

§

Research Supported by Air Force Office of Scientific Research AFSC, USAF, under Grant AFOSR 76–3109.

References

Billard, L., Lacayo, H. and Langberg, N. (1979) A new look at the simple epidemic process. J. Appl. Prob. 16, 198–202.Google Scholar
Billard, L., Lacayo, H. and Langberg, N. A. (1980) Generalizations of the simple epidemic process. J. Appl. Prob. 17(4).Google Scholar
Cox, D. R. (1962) Renewal Theory. Methuen, London.Google Scholar
Mcneil, D. R. (1972) On the simple stochastic epidemic. Biometrika 59, 494–497.Google Scholar
Ross, S. M. (1970) Applied Probability Models with Optimization Applications. Holden-Day, San Francisco.Google Scholar
Severo, N. C. (1969) Generalizations of some stochastic epidemic models. Math. Biosci. 4, 395–402.Google Scholar