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The final outcome of an epidemic model with several different types of infective in a large population

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Frank Ball  and
Damian Clancy
Frank Ball*
Affiliation:
University of Nottingham
Damian Clancy*
Affiliation:
University of Newcastle
*
∗Postal address: Department of Mathematics, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗∗Postal address: Department of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, NEI 7RU, UK.
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Abstract

We consider a stochastic model for the spread of an epidemic amongst a closed homogeneously mixing population, in which there are several different types of infective, each newly infected individual choosing its type at random from those available. The model is based on the carrier-borne model of Downton (1968), as extended by Picard and Lefèvre (1990). The asymptotic distributions of final size and area under the trajectory of infectives are derived as the initial population becomes large, using arguments based on those of Scalia-Tomba (1985), (1990). We then use our limiting results to compare the asymptotic final size distribution of our model with that of a related multi-group model, in which the type of each infective is assigned deterministically.

Keywords

CARRIER-BORNE EPIDEMICSEPIDEMICS IN HETEROGENEOUS POPULATIONSSIZE OF EPIDEMICAREA UNDER TRAJECTORY OF INFECTIVESGAUSSIAN LIMIT THEOREMSEFFECT OF VARIABILITY

MSC classification

Primary: 92D30: Epidemiology
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 3 , September 1995 , pp. 579 - 590
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Work carried out in part while Damian Clancy was supported by an SERC research studentship at the University of Nottingham.

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