Pooled testing to isolate infected individuals

The usual problem for group testing is this: For a given number of individuals and a given prevalence, how many tests T^' are required to find every infected individual? In real life, however, the problem is usually different: For a given number of individuals, a given prevalence, and a limited number of tests T much smaller than T^', how can these tests best be used? In this conference paper, we outline some recent results on this problem for two models. First, the `practical' model, which is relevant for screening for COVID-19 and has tests that are highly specific but imperfectly sensitive, shows that simple algorithms can be outperformed at low prevalence and high sensitivity. Second, the `theoretical' model of very low prevalence with perfect tests gives interesting new mathematical results.