  The original problem of group testing consists in the identification of
defective items in a collection, by applying tests on groups of items that
detect the presence of at least one defective item in the group. The aim is
then to identify all defective items of the collection with as few tests as
possible. This problem is relevant in several fields, among which biology and
computer sciences. It recently gained attraction as a potential tool to solve a
shortage of COVID-19 test kits, in particular for RT-qPCR. However, the problem
of group testing is not an exact match to this implementation. Indeed,
contrarily to the original problem, PCR testing employed for the detection of
COVID-19 returns more than a simple binary contaminated/non-contaminated value
when applied to a group of samples collected on different individuals. It gives
a real value representing the viral load in the sample instead. We study here
the use that can be made of this extra piece of information to construct a
one-stage pool testing algorithms on an idealize version of this model. We show
that under the right conditions, the total number of tests needed to detect
contaminated samples diminishes drastically.
