Is Pool Testing Method of COVID-19 Employed in Germany and India Effective?

Abstract At present, several countries, such as Germany and India, have employed a pool testing method on the nucleic acid testing of COVID-19 for the shortage of detection kits. In this method, the testing is performed on several samples of the cases together as a bunch. If the test result of the bunch is negative, then it is shown that none of the cases in the bunch has been infected with the novel coronavirus. On the contrary, if the test result of the bunch is positive, then the samples are tested one by one to confirm which cases are infected. We verified that the pool testing method of COVID-19 is effective in the situation of the shortage of nucleic acid detection kits based on probabilistic modeling. Moreover, the following interesting results are also obtained. (1) If the infection rate is extremely low, while the same number of detection kits are used, the expected number of cases that can be tested by the pool testing method is far more than that by the one-by-one testing method. (2) The pool testing method is effective only when the infection rate is less than 0.3078. While the infection rate decreases from 0.3078 to 0.0018, the optimal sample sizes in one bunch increases from 3 to 25. In general, the higher the infection rate, the smaller the optimal sample size in one bunch. (3) If N samples are tested by the pool testing method, while the sample size in one bunch is G, the number of detection kits required is in the interval (N/G, N). Additionally, the lower the infection rate, the fewer detection kits are needed. Therefore, the pool testing method is not only suitable for the situation of the shortage of detection kits, but also the situation of the overall or sampling detection for a large population.