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We need to do more testing for coronavirus. What if we could do ten times more tests, without needing any more test kits, just using maths?

This is such an important idea, and it’s being woefully underused by countries around the world. Please share this video—the more widely this simple, elegant way to fight covid is known, the better!

# Video chapters
00:00 Introduction
00:27 PCR testing
01:06 Simple pooling
04:13 2D pooling
06:43 Kirkman’s schoolgirl problem
09:10 Kirkman’s schoolgirls’ coronavirus problem
10:46 Cleverer combinatorial methods (P-BEST)
12:18 Let’s test EVERYONE
13:45 WHY IS NO-ONE DOING THIS?!?!

If you want to know more about why testing is to critical to controlling coronavirus, check out the section on test, trace and isolate in my epic covideo from April: https://youtu.be/bygIMiNnlVE?t=839

# Sources

Here are some of the sources I used when researching this video:

Preprint on 2D pooling using 96- and 384-well plates which got me excited in March: https://www.medrxiv.org/content/10.1101/2020.03.27.20043968v1

Article by one of the Rwandan mathematicians who worked on hypercube testing (though it doesn’t explicitly mention high-dimensional pooling): https://theconversation.com/rwandas-covid-19-pool-testing-a-savvy-option-where-theres-low-viral-prevalence-141704
HOT OFF THE PRESS on October 21st, the hypercube-based pooling method in Nature! https://www.nature.com/articles/s41586-020-2885-5

Kirkman’s schoolgirl problem: https://en.wikipedia.org/wiki/Kirkman%27s_schoolgirl_problem
You can read more about how to solve it here: https://cs.lmu.edu/~ray/notes/kirkman/
And you can find a cool visualisation of the solution here: https://math.stackexchange.com/a/1204049
Girls’ names selected at random from the top 10 names for each letter between 1996 and 2018 in the UK: https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/adhocs/10429babynames1996to2018englandandwales

Article on the P-BEST algorithm: https://www.nytimes.com/2020/08/21/health/fast-coronavirus-testing-israel.html
The P-BEST paper: https://advances.sciencemag.org/content/6/37/eabc5961

Paul Romer discusses his mass testing plan in this interview with the brilliant @Healthcare Triage (whose whole channel is a great source of coronavirus information): https://www.youtube.com/watch?v=H2IbrT16uJI
It’s also detailed on his website https://roadmap.paulromer.net/ and in this written interview https://www.newyorker.com/news/q-and-a/paul-romer-on-how-to-survive-the-chaos-of-the-coronavirus

Wikipedia list of places around the world using pooled testing for coronavirus: https://en.wikipedia.org/wiki/List_of_countries_implementing_pool_testing_strategy_against_COVID-19
Coronavirus testing data via the excellent Our World in Data: https://ourworldindata.org/grapher/full-list-covid-19-tests-per-day (total of 512,080,611 tests retrieved on 30/09/2020…sorry, it took me a long time to finish this video!)

# Interesting things that didn’t make it into the video

A great article on how this is the exact same maths as the game of Dobble (aka Spot It! in the US) https://puzzlewocky.com/games/the-math-of-spot-it/
Combinatorial testing without needing robots, using punched cards https://www.smarterbetter.design/origamiassays/default/instructions

# Images

Nasopharyngeal swab technique diagram via https://www.cdc.gov/vaccines/pubs/surv-manual/chpt22-lab-support.html
384-well plate image via https://www.flickr.com/photos/64860478@N05/37821508295
The pretty Victorian church is Ash Church in Kent, from a book published in 1864 https://www.flickr.com/photos/britishlibrary/11067630783/

# Errata

Obviously where I mention Kirkman triples for ‘many different combinations of total numbers of students and group sizes…’ around 08:05 mark where you see the asterisk…well, triples means a group size of three, doesn’t it? I only noticed this obvious mistake in the edit! Also, the solution was first published in 1968. Not the best fact-checked paragraph in the script…

Thanks to trifonTAF for pointing out in the comments that I slipped up describing the P-BEST algorithm: it divides samples into 48 pools *of 48 samples each*, and each sample appears in 6 pools. D’oh!

source

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