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Dynamics of an epidemic in a closed population

Part of: Stochastic processes Physiological, cellular and medical topics Limit theorems Special processes

Published online by Cambridge University Press:  01 July 2016

Åke Svensson
Åke Svensson*
Affiliation:
Stockholm University
*
∗Postal address; Department of Statistics, Stockholm University, 5106 91 Stockholm, Sweden.
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Abstract

A simple model for the intensity of infection during an epidemic in a closed population is studied. It is shown that the size of an epidemic (i.e. the number of persons infected) and the cumulative force of an epidemic (i.e. the amount of infectiousness that has to be avoided by a person that will stay uninfected during the entire epidemic) satisfy an equation of balance. Under general conditions, small deviances from this balance are, in large populations, asymptotically mixed normally distributed. For some special epidemic models the size of an asymptotically large epidemic is asymptotically normally distributed.

Keywords

EPIDEMIC MODELSCOUNTING PROCESSESMARTINGALE LIMIT THEOREMSSIZE DISTRIBUTION

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60G44: Martingales with continuous parameter 60F05: Central limit and other weak theorems 92C99: None of the above, but in this section
Type
Research Article
Information
Advances in Applied Probability , Volume 25 , Issue 2 , June 1993 , pp. 303 - 313
Copyright
Copyright © Applied Probability Trust 1993 

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