PCR, Tropical Arithmetic, and Group Testing

Polymerase chain reaction (PCR) testing is the gold standard for diagnosing COVID-19. Unfortunately, the outputs of these tests are imprecise and therefore quantitative group testing methods, which rely on precise measurements, are not applicable. Motivated by the ever-increasing demand to identify individuals infected with SARS-CoV-19, we propose a new model that leverages tropical arithmetic to characterize the PCR testing process. In many cases, some of which are highlighted in this work, tropical group testing is provably more powerful than traditional binary group testing in that it requires fewer tests than classical approaches, while additionally providing a mechanism to identify the viral load of each infected individual.