TestingThe Maths Logic That Could Help Test More People for Coronavirus
Rapid testing of patients is of great importance during a pandemic. But at a time when there aren’t enough COVID-19 tests or testing has been slow, is there a way to enhance the process? As a mathematician and engineer, I asked myself if there was anything a theoretician could do to help meet the demands of the World Health Organization to test as many patients as possible. Well, there might be a way to test many patients with a few test tubes. Instead of using one test tube to produce a result for one sample, we can use several test tubes to test many more samples – with the help of some logic. The general idea is simple. A sample taken from each of our theoretical patients is distributed to half of the test tubes that we have, in different combinations. If we have ten test tubes, for example, we would distribute the samples from each patient into a different combination of five of them. Any tube that tests negative tells us that all the patients that share that test tube must be negative. Meanwhile, test tubes that test positive could contain samples from a number of positive patients – and an individual patient will test positive only if all their associated test tubes are positive.
Rapid testing of patients is of great importance during a pandemic. But at a time when there aren’t enough COVID-19 tests or testing has been slow, is there a way to enhance the process? As a mathematician and engineer, I asked myself if there was anything a theoretician could do to help meet the demands of the World Health Organization to test as many patients as possible.
Well, there might be a way to test many patients with a few test tubes. Instead of using one test tube to produce a result for one sample, we can use several test tubes to test many more samples – with the help of some logic.
The general idea is simple. A sample taken from each of our theoretical patients is distributed to half of the test tubes that we have, in different combinations. If we have ten test tubes, for example, we would distribute the samples from each patient into a different combination of five of them.
Any tube that tests negative tells us that all the patients that share that test tube must be negative. Meanwhile, test tubes that test positive could contain samples from a number of positive patients – and an individual patient will test positive only if all their associated test tubes are positive.
This approach is efficient at the early stages of an epidemic in particular, when there are relatively few people that might test positive.
Modifying the Approach
As more patients are infected, however, identifying who has the virus is more challenging because the positively tested tubes are more likely to include even greater combinations of patients. To overcome this difficulty, the approach has to be modified as illustrated in the example below.
Say that we have six test tubes and 20 patients. And the test tubes are ordered and numbered as #1, #2, #3, #4, #5, and #6. Each patient is given a six-digit number made up of zeros and ones (a binary system). Each digit corresponds to a test tube – a “0” means we don’t add the sample to the corresponding test tube, whereas a “1” means that we do.
