  Repeated asymptomatic screening for SARS-CoV-2 promises to control spread of
the virus but would require too many resources to implement at scale. Group
testing is promising for screening more people with fewer test resources:
multiple samples tested together in one pool can be excluded with one negative
test result. Existing approaches to group testing design for SARS-CoV-2
asymptomatic screening, however, do not consider dilution effects: that false
negatives become more common with larger pools. As a consequence, they may
recommend pool sizes that are too large or misestimate the benefits of
screening. Modeling dilution effects, we derive closed-form expressions for the
expected number of tests and false negative/positives per person screened under
two popular group testing methods: the linear 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 testing protocol practitioners can use for mitigating
COVID-19. In a case study, we demonstrate the effectiveness of this methodology
in controlling spread.
