Optimizing Pool Size for Pool Testing of SARS-CoV-2

Jerry Li

One evening in the summer of 2020, well after the severity and endurance of the COVID-19 pandemic had become evident, I was having a chat with my father at the dinner table. Both STEM people, our talks often leaned towards the topic of science, especially in the realm of current events. This time, it was the matter of COVID testing that made its appearance. Testing, so essential to managing an outbreak, yet so scarce when it was needed. That night, I learned about a mostly unemployed method in the pandemic called “pooled testing,” where, rather than testing polymerase chain reaction (PCR) samples individually, multiple are combined and tested together. In theory, if a pooled sample were to test negative, it would indicate that all individual samples of that pool are also negative, meaning many tests can be saved. So why not squeeze as many samples as possible (without jeopardizing accuracy) into each pool? The issue here is that with so many samples per pool, more pools are likely to test positive, and all individuals of positive pools must be retested to identify those with the disease. This posed an interesting problem. If some balance between too many and too few individuals per pool could be found, then the amount of tests and thus resources/money saved could be greatly boosted … Over the course of my project, which spanned from late fall of 2020 to summer of 2021 (with large pauses in between), I received advice from a mentor on the process of reviewing literature, producing novel contributions in the field, and writing a paper. However, my research and derivations were performed almost exclusively from the desk in my room. But even without an extravagant lab or experiments to run, this intersection of science and mathematics and public health was enough to fully entertain me.