Source: Adv. in Appl. Probab.
Volume 43, Number 4
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.
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