  During the COVID-$19$ pandemic the health authorities at airports and train
stations try to screen and identify the travellers possibly exposed to the
virus. However, many individuals avoid getting tested and hence may misreport
their travel history. This is a challenge for the health authorities who wish
to ascertain the truly susceptible cases in spite of this strategic
misreporting. We investigate the problem of questioning travellers to classify
them for further testing when the travellers are strategic or are unwilling to
reveal their travel histories. We show there are fundamental limits to how many
travel histories the health authorities can recover.% can be correctly
classified by any probing mechanism.
