  In epidemic or pandemic situations, resources for testing the infection
status of individuals may be scarce. Although group testing can help to
significantly increase testing capabilities, the (repeated) testing of entire
populations can exceed the resources of any country. We thus propose an
extension of the theory of group testing that takes into account the fact that
definitely specifying the infection status of each individual is impossible.
Our theory builds on assigning to each individual an infection status
(healthy/infected), as well as an associated cost function for erroneous
assignments. This cost function is versatile, e.g., it could take into account
that false negative assignments are worse than false positive assignments and
that false assignments in critical areas, such as health care workers, are more
severe than in the general population. Based on this model, we study the
optimal use of a limited number of tests to minimize the expected cost. More
specifically, we utilize information-theoretic methods to give a lower bound on
the expected cost and describe simple strategies that can significantly reduce
the expected cost over currently known strategies. A detailed example is
provided to illustrate our theory.
