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Nitya Nigam The global COVID-19 pandemic continues to rage on, with the total number of cases around the world having just hit 13 million. In addition to mask-wearing and social distancing, scientists have highlighted widespread testing as an important measure in reducing the spread of the coronavirus. However, many regions do not have sufficient equipment and chemicals to run individualised tests. For this reason, the mathematical strategy of group testing has been suggested as a way to quickly test a large number of patients without using up an excess of precious testing materials. Group testing involves mixing samples of several people together, and then testing the mixture in one go. If this test comes back negative, then all of the people whose samples went into the mixture are marked as negative at once, saving time and resources. However, if this test comes back positive, further testing is required to pinpoint the infected individuals. There are four main techniques to do this. Method 1 involves samples being mixed together in groups of equal sizes, and then these mixtures are tested separately. If a group tests positive, then each individual member of the group is retested. This method was used in Wuhan, China in May, as part of efforts to test the majority of the city's population, identifying 56 infected people from about 2.3 million individuals involved in testing. This method works best in low levels of infection (about 1% of the population), because group tests are likely to be negative. Method 2 is a more sophisticated version of Method 1, which adds more rounds of group tests before testing individuals separately. However, both of these approaches are quite slow, as it takes several hours to get the results for each group test. These group results must be known before further testing can occur to pinpoint individual infections. “This is a fast-growing, fast-spreading disease. We need answers much faster than this approach would allow,” says Wilfred Ndifon, a theoretical biologist based in Rwanda. Ndifon and his colleagues at the African Institute for Mathematical Sciences have improved on these strategies, aiming to reduce the number of tests needed. Their first round of group tests is the same as described above, but for positive-testing groups, they propose a different method. Imagine a 3x3 grid, where each cell represents one person’s sample. The samples in each row and column are tested as one group, meaning there will be 6 total tests, and each individual will have been tested twice. If an individual sample is positive, it will cause both groups it is part of to be positive, making it easy to find the individual. The dimensionality of testing can be increased from a square grid to a cube, which allows for bigger groups and higher efficiency. This constitutes Method 3. Although Method 3 decreases the number of tests that must be conducted, some scientists say that even two rounds of testing take too much time. Manoj Gopalkrishnan, a computer scientist at the Indian Institute of Technology Bombay, has proposed a one-step solution that is our Method 4. His approach involves mixing samples in different groups, using a counting technique known as Kirkman triples, to determine how the samples should be distributed. Imagine a grid in which each row represents one test, and each column represents one person. In general, each test should have the same number of samples, and each individual’s sample should be tested the same number of times. This method requires more tests to achieve the same level of accuracy as the previous methods and also means working with a large number of samples at once. However, it significantly decreases the amount of time taken to test a large group of people. Let us know in the comments if you enjoyed this article, and what your thoughts on group testing are!
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