Advances in Applied Probability

Threshold behaviour of emerging epidemics featuring contact tracing

Frank G. Ball, Edward S. Knock, and Philip D. O'Neill

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 43, Number 4 (2011), 1048-1065.

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.aap/1324045698

Digital Object Identifier
doi:10.1239/aap/1324045698

Mathematical Reviews number (MathSciNet)
MR2867945

Zentralblatt MATH identifier
1229.92067

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

Keywords
Stochastic epidemic contact tracing branching process reproduction number

Citation

Ball, Frank G.; Knock, Edward S.; O'Neill, Philip D. Threshold behaviour of emerging epidemics featuring contact tracing. Adv. in Appl. Probab. 43 (2011), no. 4, 1048--1065. doi:10.1239/aap/1324045698. https://projecteuclid.org/euclid.aap/1324045698


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