One-Shot Pooled COVID-19 Tests via Multi-Level Group Testing

A key requirement in containing contagious diseases, like the COVID-19 pandemic, is the ability to efficiently carry out mass diagnosis over large populations, especially when testing resources are limited and rapid identification is essential for outbreak control. Some of the leading testing procedures, such as those utilizing qualitative polymerase chain reaction, involve using dedicated machinery which can simultaneously process a limited amount of samples. A candidate method to increase the test throughput is to examine pooled samples comprised of a mixture of samples from different patients. In this work, we study pooling-based tests which operate in a one-shot fashion, while providing an indication not solely on the presence of infection, but also on its level, without additional pool-tests, as often required in COVID-19 testing. As these requirements limit the application of traditional group-testing (GT) methods, we propose a multi-level GT scheme, which builds upon GT principles to enable accurate recovery using much fewer tests than patients, while operating in a one-shot manner and providing multi-level indications. We provide a theoretical analysis of the proposed scheme and characterize conditions under which the algorithm operates reliably and at affordable computational complexity. Our numerical results demonstrate that multi-level GT accurately and efficiently detects infection levels, while achieving improved performance and less pooled tests over previously proposed oneshot COVID-19 pooled-testing methods. Our simulations show that the efficient method proposed in this work can correctly identify the infected items and their infection levels with high probability at the known upper bound (for a maximum likelihood decoder in GT) on the number of tests. We also show that the method works well in practice when the number of infected items is not assumed to be known in advance.