Fig 1.
An illustration of finding cases in a pool.
Demonstrated for a pool of eight samples for individual testing (A), 2-level pooling (B), binary splitting (C), and Sobel-R1 (F). For recursive binary splitting (D), we show part of the search tree highlighting the difference to binary splitting. For Purim (E), we show the search for three cases in an overall set of 82 = 64, starting from 16 pools of size eight (i.e. 8 horizontal and 8 vertical in a matrix arrangement) before testing the cross-sections.
Fig 2.
The best pool size (lowest total time) depends on the infection rate, here for ir = 1%, 10%, 20%.
For low infection rates, all methods but 2-level pooling prefer pool sizes that are as large as possible. With increasing infection rate, the optimal pool size decreases—with the exception of the Sobel-R1 method—until they approach pool size 1. Parameters: sensitivity p = 0.99, false positive rate q = 0.01, population 50, 000, test duration 5h, averaged over 10 runs. Blue: individual testing; orange: 2-level pooling; green: binary splitting; red: recursive binary splitting; purple: Purim; brown: Sobel-R1.
Fig 3.
Screening the whole population.
Parameters: sensitivity p = 0.99, false positive rate q = 0.01, test duration 5h, averaged over 10 runs. Optimal (max.) pool size each (c.f. Fig 2); for ir = 1% as in (B)–(D) we obtain individual testing: 1; 2-level pooling: 12; binary splitting: 32; recursive binary splitting: 32; Purim: 32, Sobel-R1: 31. (A): Expected number and standard deviation of identified cases per test for different infection rates with optimised pool sizes; right: zoom-in for small infection rates, (B): Expected time in days and standard deviation to test the whole population depending on daily test capacity per 1m population, infection rate 1%; right: zoom-in excl. individual testing, (C): Expected true positives and false positives for the six methods (pop. 100,000), (D): Numbers of identified cases and quarantined individuals (pop. 100,000).
Table 1.
Data used in the simulations based on country.
Table 2.
Expected time in days to test 10% of the US population for three different infection rates.
Table 3.
Effectiveness of conducting 100,000 tests on a population of 1 million; full statistics over 10 simulations each.