Before revision:  These challenges can be mitigated by extensive testing. We study testing policies that optimize a fixed budget of tests within a single institution (e. g., business, school, nursing home, etc.) by varying the number of batches that the tests are split into. We prove that, in an exponential spread model and for reasonable parameter values, the expected size of an outbreak at initial detection is smaller when random subgroups of the population are tested frequently, as opposed to periodic testing of the entire population.
After revision:  These challenges can be mitigated through testing, testing budget is often limited. Here we study how institutions, such as nursing homes, should utilize a fixed test budget for early detection of an outbreak at initial detection is smaller when random subgroups of the population are tested frequently, as opposed to periodic testing of the entire population.