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Threshold behaviour of emerging epidemics featuring contact tracing

Part of:Markov processes

Published online by Cambridge University Press:  01 July 2016

Frank G. Ball,
Edward S. Knock and
Philip D. O'Neill
Frank G. Ball*
Affiliation:
University of Nottingham
Edward S. Knock*
Affiliation:
University of Nottingham
Philip D. O'Neill*
Affiliation:
University of Nottingham
*
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
∗ Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK.
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Abstract

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This paper is concerned with a stochastic model for the spread of an epidemic with a contact tracing scheme, in which diagnosed individuals may name some of their infectious contacts, who are then removed if they have not been already. Traced individuals may or may not also be asked to name their own contacts. The epidemic is studied by considering an approximating, modified birth-death process with intersibling dependencies, for which a threshold parameter and expressions from which extinction probabilities may be calculated are derived. When all individuals can name their contacts, it is shown that this threshold parameter depends on the infectious period distribution only through its mean. Numerical studies show that the infectious period distribution choice can have a material effect on the threshold behaviour of an epidemic, while the dependencies help reduce spread.

Keywords

Stochastic epidemiccontact tracingbranching processreproduction number

MSC classification

Primary:92D30: Epidemiology
Secondary:60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011, pp. 1048 - 1065
Copyright
Copyright © Applied Probability Trust 2011 

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