Here is the code I used to create the graphics found in the Cornell Data Journal Article “The elegant geometry behind Rwanda’s COVID-19 pooled testing strategy”.
The graphics were created with the library Isomer.js. To run the code, paste the contents of the playground.js file in the Isomer Playground.
I first became interested in pooled testing for COVID-19 in April after seeing a Facebook post about it in the Facebook group Open Source Medical Supplies. After a quick Google search, I found the paper A strategy for finding people infected with SARS-CoV-2: optimizing pooled testing at low prevalence (arXiv). Since then, it has been peer-reviewed and published in Nature. I found the paper to be really approachable, and I hoped to share it with a broader audience with my visualiations.
The reason why I used cubes of length 3 in my CDJ article is because the paper determines that at a low prevalence, the optimal size of a hypercube is of dimension 4 and length 3. Smaller hypercubes are less efficient because fewer samples are tested at a time. Larger hypercubes are also less efficient because they run the risk of having multiple positives in the same hypercube. This requires an additional round of testing to be used.
In the example used in the section titled “Applying this to the real world”, the average number of samples testing positive was calculated to be 8.35. This was done with a Poisson distribution centered at 9 / 74. For each sample, the random variable is the number of positive samples in a given pool. I took the probability that the random variable was greater than or equal to one.
In addition, the expected value of the number of tests required to find a sample was calculated to be 12.081. The reasoning behind this calculation is found in Appendix F in the research paper.