Before revision:  We show that under a broad set of early-outbreak scenarios, given a certain budget of tests, increasing testing frequency of random samples of the population will reduce the societal risk, defined as the number of infection opportunities until first detection. For example, testing a quarter of the institution members every week is generally better than testing the entire institution every month.
After revision:  We show that under a broad set of early-outbreak scenarios, given a certain budget of tests, it is generally better than testing the entire institution every month.