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On the asymptotic size and duration of a class of epidemic models

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

Published online by Cambridge University Press:  14 July 2016

Åke Svensson
Åke Svensson*
Affiliation:
Stockholm University
*
∗Postal address: Department of Mathematical Statistics, Stockholm University, S-106 91 Stockholm, Sweden.
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Abstract

Models for epidemic spread of infections are formulated by defining intensities for relevant counting processes. It is assumed that an infected individual passes through k stages of infectivity. The times spent in the different stages are random. Many well-known models for the spread of infections can be described in this way. The models can also be applied to describe other processes of epidemic character (such as models for rumour spreading). Asymptotic results are derived both for the size and for the duration of the epidemic.

Keywords

COUNTING PROCESSESMARTINGALE LIMIT THEOREMSSIZE DISTRIBUTIONASYMPTOTIC DURATION

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 Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 11 - 24
Copyright
Copyright © Applied Probability Trust 1995 

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