Group Testing During the COVID-19 Pandemic: Optimal Group Size Selection and Prevalence Control

Lin, Yifan; Ren, Yuxuan; Wan, Jingyuan; Zhou, Enlu

Group testing pools multiple samples together and performs tests on these pooled samples to discern the infected samples. It greatly reduces the number of tests, however, with a sacrifice of increasing false negative rates due to the dilution of the viral load in pooled samples. Therefore, it is important to balance the trade-off between number of tests and false negative rate. We explore two popular group testing methods, namely linear array (a.k.a. Dorfman's procedure) and square array methods, and analyze the optimal group size of a pooled sample that minimizes the group false negative number under a constraint of testing capacity. Our analysis shows that when there is reasonably large testing capacity, the linear array method yields smaller false negative number and hence is preferred. When the testing capacity is small, square array method is more feasible and preferred. In addition, we consider testing a closed community in a period of time and determine the optimal testing cycle that minimizes the final prevalence rate of infection at the end of the time period. Finally, we provide a testing protocol for practitioners to use these group testing methods in the COVID-19 pandemic.