Before revision:  Dorfman's procedure) and square array methods , and analyze the optimal group size of a pooled sample that minimizes the group false negative number under a constraint of testing capacity. Our analysis shows that when there is reasonably large testing capacity, the linear array method yields smaller false negative number and hence is preferred. When the testing capacity is small, square array method is more feasible and preferred. In addition, we consider testing a closed community in a period of time and determine the optimal testing cycle that minimizes the final prevalence rate of infection at the end of the time period.
After revision:  Dorfman's procedure) and square array methods . We find that test error correlation induced by a common viral load across an individual's samples results in many fewer false negatives than would be expected from less realistic but more widely assumed independent errors. This insight also suggests that false positives can be controlled through repeated tests without significantly increasing false negatives. Using these closed-form expressions to trace a Pareto frontier over error rates and tests, we design testing protocols for repeated asymptomatic screening of a large population. We minimize disease prevalence by optimizing a time-varying pool sizes and screening frequency constrained by daily test capacity and a false positive limit. This provides a closed community in a period of time and determine the optimal testing cycle that minimizes the final prevalence rate of infection at the end of the time period.