Copyright © 2016 - 2020, The Troy Press
Copyright © 2016 - 2020, The Troy Press
IMAGE: This image came from Worldmeter, cited below.
Some of you are aware I'm an Earth scientist and have been applying my scientific modeling skills to the SARS-CoV-2 virus's outbreak pandemic - known as Covid-19 - and I've already published a lot of that modeling. But that work was only worthwhile under assumptions that include that nothing effective was being done about the virus's spread. The data shows that's changed. So, the original model isn't as useful as it was a month ago, and so I turned my attention to the doubling curve since it directly reflects both where we've been and where we're going.
Simply, the daily change in the number of new cases defines a rate of change which is a clear indicator of whether the pandemic is spreading faster or slower and looking at the "doubling rate" is a very direct way to observe this dynamic.
AT RIGHT: This chart is only for the USA and clearly the trend is improving. Now is NOT the time to stop with self quarantine / social-distancing.
To be clear: There are two viewpoints at any point in time 1) Looking back, how many days did it take for the number of cases to double? And; 2) Looking forward, how many days at the current rate will it take for the current number of cases to double? Both are interesting and informing. So, I address them both in my work.
I've been collecting data for Covid-19 confirmed cases in the USA since the first cases in the USA in early March. At that time, it wasn't clear where the best sources were, and, as I note below, the numbers collected were problematic. However, in the second week of March, as the number of cases in the USA crossed over 1000, I found what I believe to be the best data source, which is this site, and I've been collecting data from them every day at noon, Pacific Time:
Best Data Source: Worldmeters
And, by the way, this site makes most all of its data available for free to anyone, so you are all free to double check my work. ... I don't claim there's no bugs, so if you find something "wrong", please do let me know - politely, please - I'd like to fix it so it's damned good. Note that the code DOES use rounding to the nearest decimal place shown, so please don't complain about that! ... You can reach me at Art at TheTroyPress dot Com - or, here sometimes!
In the early part of March, the line was logarithmic, but that was probably due to testing and reporting anomalies - remember, 1 is an infinite percent increase over zero! And so the initial numbers plotted a crazy line, but the numbers soon settled into a good data pattern and became approximately representing a hyperbola - the kind described first by Menaechmus, not the crap definition you'll likely find online - and then, a bit later, the line changed again. In my work, the first days simply aren't useful, and this begins when the good data starts to take shape.
This work is rather simple, but very informative:
- In looking back, it's pretty straight-forward to take any particular date and look back at the data and calculate, for that date, how many days in the past had half that number of confirmed cases. Simple, right? ... I add in the extra work to calculate partial days... And;
- In looking forward, it's pretty straight-forward to look at the change in the last day and from that "delta" project forward from there with the presumption the rate doesn't change. Of course the rate WILL change (at least we hope so!) but we don't know what that rate is or will be, so we just project what it will take with the change from this date to the immediately preceding date to double from where we are today. Simple, right? Again, I calculate partial days - not hard to do.
Yes, this decidedly is NOT rocket science.
Now, here's the output run, including data starting on March 11 through to today and it includes the case data for each date (so yall looking to double-check me can just scarf the data from here, though it doesn't include the earlier data), though the program rightly rejects projections earlier than it does because they don't make sense. Below this, I have some additional commentary on properly understanding what the data tells us. To wit:
For 2020/3/14 2488 cases is double from 1 days past & doubles in 4 days.
For 2020/3/15 3244 cases is double from 1.7 days past & doubles in 8.6 days.
For 2020/3/16 4138 cases is double from 2.3 days past & doubles in 9.3 days.
For 2020/3/17 5894 cases is double from 2.4 days past & doubles in 6.7 days.
For 2020/3/18 7324 cases is double from 2.5 days past & doubles in 10.2 days.
For 2020/3/19 11335 cases is double from 2.1 days past & doubles in 5.7 days.
For 2020/3/20 16638 cases is double from 1.8 days past & doubles in 6.3 days.
For 2020/3/21 23480 cases is double from 1.9 days past & doubles in 6.9 days.
For 2020/3/22 31057 cases is double from 2.2 days past & doubles in 8.2 days.
For 2020/3/23 41511 cases is double from 2.4 days past & doubles in 7.9 days.
For 2020/3/24 49760 cases is double from 2.8 days past & doubles in 12.1 days.
For 2020/3/25 61167 cases is double from 3.1 days past & doubles in 10.7 days.
For 2020/3/26 76514 cases is double from 3.3 days past & doubles in 10 days.
For 2020/3/27 94238 cases is double from 3.3 days past & doubles in 10.6 days.
For 2020/3/28 115547 cases is double from 3.3 days past & doubles in 10.8 days.
For 2020/3/29 135184 cases is double from 3.6 days past & doubles in 13.8 days.
For 2020/3/30 155923 cases is double from 3.9 days past & doubles in 15 days.
For 2020/3/31 177452 cases is double from 4.3 days past & doubles in 16.5 days.
For 2020/4/1 205438 cases is double from 4.6 days past & doubles in 14.7 days.
For 2020/4/2 236339 cases is double from 4.9 days past & doubles in 15.3 days.
For 2020/4/3 266279 cases is double from 5.1 days past & doubles in 17.8 days.
For 2020/4/4 302147 cases is double from 5.2 days past & doubles in 16.8 days.
For 2020/4/5 329280 cases is double from 5.6 days past & doubles in 24.3 days.
For 2020/4/6 356414 cases is double from 6 days past & doubles in 26.3 days.
For 2020/4/7 383256 cases is double from 6.5 days past & doubles in 28.6 days.
For 2020/4/8 424945 cases is double from 6.8 days past & doubles in 20.4 days.
For 2020/4/9 454615 cases is double from 7.3 days past & doubles in 30.6 days.
For 2020/4/10 486490 cases is double from 7.8 days past & doubles in 30.5 days.
For 2020/4/11 521365 cases is double from 8.2 days past & doubles in 29.9 days.
For 2020/4/12 550655 cases is double from 8.7 days past & doubles in 37.6 days.
For 2020/4/13 586941 cases is double from 9.2 days past & doubles in 32.4 days.
For 2020/4/14 603496 cases is double from 10 days past & doubles in 72.9 days.
For 2020/4/15 623669 cases is double from 10.6 days past & doubles in 61.8 days.
For 2020/4/16 667572 cases is double from 10.8 days past & doubles in 30.4 days.
For 2020/4/17 690900 cases is double from 11.4 days past & doubles in 59.2 days.
Now, the doubling looking backwards might not seem so great, but the number of days to doubling steadily rising - that's proof right there that what we're doing in the USA is having a positive impact. Of course, if it keeps doubling every 11 days or so, that's clearly bad. BUT, in the previous 11 days we've cut the doubling rate in half. If we keep this up, it won't take that long before the curve isn't rising at all, which is what we all want. And, indeed, looking at the future, the projections are even more encouraging.
For now, ignore the totals and focuse on the curves - the change over time! Yes, the totals are disturbing, but we're "flattening the curve" quite successfully - keep reading.
Now look at the FUTURE doubling times and they're a lot more encouraging.
Most encouraging is that in the last nine (9) days, we've seen the doubling rate at at least a month or more, with a few projections to more than two months! Of course, because the rate of change between any pair of days makes the rate seem to jump around, this is just a reflection of the fact that the rate of increase in cases is dropping steadily and dramatically. We still have problems with not enough testing and also reporting issues, but we're all doing the best we can. Still, when the doubling rate changes from 2.3 days a month ago, into a projected 30+ days for about the last week, I think this is cause for recognition that all the pain from this sequestration / shelter-in-place / lock-down is working and is saving lives.
Now is NOT a time to relax. We have to drive this down further, but...
...we're now looking at the light at the end of the proverbial tunnel - now's not the time to stop and let it become the lamp of an oncoming train!