Before revision:  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. We also simulate the effect of different policies in a network SEIR modeltaking into account factors such as variable connectivity between individuals, incubation period, and inaccurate testing results. 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.
After revision:  We prove that, in an exponential spread model and for reasonable parameter values, the expected size of an outbreak . Using an extended network-SEIR model, we show that 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.