Estimating lock down duration
Amidst this covid 19 breakdown, most countries have resorted to lockdowns for certain X days. I wanted to understand how to estimate a lock-down period.
So all the calculations in the following article are based around Indian population and some sort of logical guesses. Let’s begin.
We will do a series of assumptions and intentionally will do a rough worst case estimate to incorporate practical factors, inefficiencies and factors beyond our scope of understanding, more importantly try to keep things simple.
Total population in India = 1.3B people
There is approx. 1 hospital per district in India. But still not all hospitals have approved covid-19 testing facility, although there might be private testing firms but still they might not be available in every district. So we need to assume a factor that reduces overall processing capacity to accommodate the cost of transportation of samples, storage etc. Let’s assume it brings down the capacity to 75%.
Now each lab is capable of processing roughly 5000–8000 results/day (4). Let’s take average 6500 results/day.
Effective processing capacity/district = 0.75 * 6500 = 4875 results/day/district.Number of districts in India = 718
Population/district =~1M people/district
There are 200 healthcare workers per 100,000 people, that means about 2000 healthcare workers per district.(2)
Let’s call healthcare workforce as HWF from now on.
Let’s say we want to sample people faster, so we dedicate 1800 HWF on the front-line for collecting samples and rest 200 on stand-by for other situations.
Population density in India is 420 people/sq km.
Let’s assume every HWF is able to collect samples from 50% people per sq km which is 210 samples/day.
Total HWF collecting samples = 1800
Samples collected/day = (210*1800) = 378,000 samples/day/district
Days required to collect samples of entire population/district = (1M people/district)/ (378,000 samples / day) = ~3 days/district
Let’s take different cases.
Case 1: Manual sample collection and entire population is sampled and processed. During this entire process everything is under lockdown.
Samples incoming/day = 378,000 samples/day
No of days samples need to be collected to cover population/district = 3days
Total samples collected = 3days * 378,000 samples/day = ~1M samples (approx. same as population per district)
Days required to process all samples (aka Lockdown period required)= (Samples)/(Results/day) = 1M/4875 = 205 days (6–7 months)
6–7 months lockdown is too long and hence it highlights that the strategy to test every person in the country as big as India is impractical and economically not viable.
Let’s assume we manage to come up with a take-at-home test kit which will have a certain amount of false positive rates (fpr). There could also be a scenario where people didn’t perform the test properly, hence we should also consider false negative rates (fnr). Let’s assume the typical manufacturing capacity of these test-kits is roughly 4000 per day (5). Let’s assume the govt. devices a way to collect results and use these results to determine lock down period in addition to it’s previous strategy of sampling people. Now because of fpr and fnr, take-at-home result data might not be reliable. So let’s say the result sample aways has 5 % error. The govt. would most likely have to random sample certain population certain number of times to overcome this error in data. We rely on the fact that the tests in hospitals are 100% accurate.
Case2: Take-home test kits and random sampling of population
Kits manufactured per day per production unit = 4000kits/day/unit
Let’s assume we setup 10 such production units.
Kits manufactured per day = 10*4000 = 40,000 kits/day
Days required to manufacture kits for everyone in a district = 1M/40,000 = 25 day.
Let’s say everyone is able to take test and report result effectively in 1–2 days, so its safe to assume within 30 days we will have test-kit result data of entire district. This is roughly 1M result data per district and as our error rate is 5 % that means 50,000 of these results might be inaccurate.
We know our on-field sampling capacity is 378,000 samples/day/district.
But instead of sampling 1M people, we will random sample approx 50,000 people let’s say thrice in a month (once beginning of month, middle of month and end of month). Why a month? Because the time taken to get all take-at-home test result is 1 month.
Days required to collect all samples in a district = 50,000/378,000 samples/day=< 1 day
Total samples collected randomly/month = 3 * 50,000 = 150,000 samples
Effective sample processing capacity/day/district = 4875 results/day/district
Days required to get results of random sampling exercise = 150,000/4875 = ~30 days
So effectively 40–45 days lock down is required as the last batch of sampling collected will take 20 days to be processed.
So what happened here? The reduction from 200 days lock-down to a 45 days lock-down was significant. Making a take-at-home test drastically reduced the lockdown period required.
What will happen if we increase our take-at-home test production capacity? And what if we add more labs equipped to accurately test covid19 cases? If we double our labs and 5x our test-kit manufacturing capacity and run awareness campaigns for people to take tests properly at home which can bring down the error rate from 5% to let’s say 2%.
Random sampling required = 2% of 1M = 20,000 samples
Total samples required(begin, middle, end)= 3 * 20,000 = 60,000 samples
Time taken to process all random sampled tests = 60,000/(2 * 4875) = 6 days
Time taken to get results for all take-at-home tests ~ 5 days
Effective lockdown ~ 11 days
The discrepancy between take-at-home result vs the random sample can be used to apply selective lock-down.
Disclaimer: The above can be highly inaccurate. I just attempted to calculate roughly based on logical guesses. The sole purpose of the article is to do an mental estimation exercise.
2. https://www.who.int/hrh/resources/16058health_workforce_India.pdf
3. https://visualize.data.gov.in/?inst=39c05e0a-e428-46f3-aacd-0dbb1d51f65e
5. https://www.thephuketnews.com/covid-19-rapid-test-kit-ready-for-trials-75320.php
