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On the normal convergence of a class of simple batch epidemics

Published online by Cambridge University Press:  14 July 2016

Naftali A. Langberg
Naftali A. Langberg*
Affiliation:
The Florida State University
*
∗Postal address: Department of Statistics, The Florida State University, Tallahassee, FL 32306, U.S.A.
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Abstract

A group of n susceptible individuals exposed to a contagious disease is considered. It is assumed that at each instant in time one or more susceptible individuals can contract the disease.

The progress of this epidemic is modeled by a stochastic process Xn(t), t in [0,∞) representing the number of infective individuals at time t. It is shown that Xn(t), with the suitable standardization and under a mild condition, converges in distribution as n → ∞to a normal random variable for all t in (0, t0), where t0 is an identifiable number.

Keywords

SIMPLE BATCH EPIDEMICSWEAK CONVERGENCECONVERGENCE IN DISTRIBUTIONNORMAL DISTRIBUTIONSBROWNIAN MOTIONBERRY–ESSEEN BOUND
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 31 - 41
Copyright
Copyright © Applied Probability Trust 

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Footnotes

Research supported by the U.S. Army Research Office, Durham, under Grant No. DAAG29–79–C–0158.

References

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