Identification-Detection Group Testing Protocols for COVID-19 at High Prevalence

Group testing allows saving chemical reagents, analysis time, and costs, by testing pools of samples instead of individual samples. We introduce a class of group testing protocols with small dilution, suited to operate even at high prevalence ($5\%-10\%$), and maximizing the fraction of samples classified positive/negative within the first round of tests. Precisely, if the tested group has exactly one positive sample then the protocols identify it without further individual tests. The protocols also detect the presence of two or more positives in the group, in which case a second round could be applied to identify the positive individuals. With a prevalence of $5\%$ and maximum dilution 6, with 100 tests we classify 242 individuals, $92\%$ of them in one round and $8\%$ requiring a second individual test. In comparison, the Dorfman's scheme can test 229 individuals with 100 tests, with a second round for $18.5\%$ of the individuals.
Comment: 11 pages, 4 figures