day-over-day total infections
Growth-factor or Increase, in per cents,
into Tenfold 10x factor, or Naive Thousand-fold 1,000x factor, in Days
How to use:
- Find last night midnight's Total Infections Count for your region.
And find the day before's, again for midnight.
(Note that it's important to get these as official counts measured at the same time, 24 hours apart.
Because the numbers are changing so fast, if you use one day's count
that was measured in the afternoon, and another day's count that was measured in the morning, for instance,
the 24-hr spread is going to be either too high or too low.)
- Divide the newer number by the other number that's one day older.
Express this in terms of a per centage. That's your day-over-day Growth Factor.
If you wish, you may subtract 100% from this number, to get the day-over-day Increase.
No difference, just some people feel more comfortable looking at Increases.
(Note: As mentioned, it's important to make sure you're looking at a 24-hr next day difference.
If you miss a day and have to look at numbers that are two days apart, not one day,
then you have to take the square root of the resulting quotient. You're not allowed to average.
And if you miss two days, so that you're looking at a pair of numbers that are
three days apart, then you'll have to take the cube root instead.
You probably don't want to do this, so just make sure your measurements are
24 hrs, only one day apart.)
(And: The Increase expressed as a decimal instead of a per centage is the "Apparent Beta." Same number.
If you want to get the Increase in percents, just multiply the Apparent Beta by 100.)
- Look up the Growth Factor or Increase on this table, and find the Tenfold 10x, description,
and Naive 1,000x results, in days.
- The 10x will give you the number of days you have to wait
until your total infections number in your region multiplies itself by 10,
assuming there are no major changes to the situation (new laws, curfews, hospital closings, etc.).
Of course you remember it's easy to multiply by 10; you just write down the number,
then add an extra zero onto the end.
- And the Naive 1,000x will give you roughly the number of days that you'll have to wait
until your total infections number in your region multiplies itself by 1,000.
Of course it's easy to multiply by 1,000, too; you just write down the number,
and then add three extra zeroes onto the end.
- Why do we call it the "Naive 1,000x"? This number gives a good first approximation,
but there are several second-order effects we have to take into account in order to use this for real:
- This works well as long as the result is less than around 25% of the population.
But once it gets up around 50% or 75% of the population, there is
something like a "terminal velocity" that starts to slow down the spreading rate
of the virus by a half or three-quarters, and it takes a bit longer.
However, if you've got more than 25% of your population infected already,
you've got worse things to worry about, so practically it makes little difference.
- Of course, if the 1,000x explodes larger than all of the adults in your population,
then it's going to hit a ceiling. You can't infect more people than you have.
So let's do an example. On Mar 16th, 2020, New York City (NYC) had a midnight total of 464 infections.
And just the previous midnight, it had a total of only 269 infections.
(464/269) = 1.725, or a Growth of 172.5%, or an Increase of 72.5%,
or an Apparent Beta of 0.725.
All the same number. Pretty easy.
We look up 172% in the table, and find that it has a 10x of 4.3 days,
and a naive 1,000x of 13 days.
Did this work out?
4.3 days forward from Mar 16 was somewhere between Mar 20 and Mar 21st.
We'd expect to end up with 464 x 10 = 464(0) = 4,640 total infections, give or take.
10 times sure sounds like a lot. How'd we do?
New York City actually increased its rate on the next days to 200%, above 172%.
So NYC actually hit 3,954 on Mar 19th, and 5,683 on Mar 20th--bracketing our expected 4,640 a day early.
But what about the 1,000x? Could 464 really grow to 4,640 in four days,
and then 46,400 in another four days, and then 464,000 in another four days?
It seems too bizarre to contemplate!
But someone was on the ball in NYC, and this is why people were going ape-ape bananas at this time.
Due to intense publicity campaigns, people self-isolated--the situation changed significantly--
and they reduced the growth factor to 120%.
120% has a 10x ten-fold factor of 12 days. Sure enough,
NYC cases didn't reach ~46,000 until Apr 1st, twelve days later,
not four days later. Woohoo! The curve has been flattened!
By an extra eight days. Slow hand clap. Please excuse me if I don't sound
as enthusiastic as some of our leaders do.
But of course it can't possibly keep on going to 464,000 now, now that we've come
so far. That would be inconceivable.
You keep using that word. I do not think it means what you think it means.
Just because perhaps you might not be able to imagine it in your mind, doesn't mean that
it's not going to happen in reality. Through much diligence, New York City has
reduced its growth rate to around 110%, as of Apr 2, 2020. That's a 10x factor of
around three-and-a-half weeks, call it four to be polite. The 50-ton big-rig
has jammed on its brakes and is starting to skid, leaving burned-rubber tracks
all over the highway with a hideous squealing sound, but it's a train wreck in very
slow motion. There could be a miracle, the situation continues to hunker down further,
and "somehow" it could come to a stop before splatting into the granite wall.
Or, the situation could remain largely unchanged, in which case 464,000 cases
by the end of April would seem pretty well guaranteed, at least by our simulation's math.
(Of course, it doesn't stop there; the following month tries for 4.6M.)
Or, New Yorkers could get tired of staying indoors, the growth factor could
easily go back up to 172% again with a 10x of 4 days, and it could easily
jump directly to 464,000 in four days and then 4.6 Million infections in the next four days again,
if people don't understand and don't keep their eyes on the ball.
To put this into perspective, NYC currently has 23,000 staffed hospital beds, plus perhaps another
4,000 emergency surge beds. If we do hit 464,000 infecteds by the end of April,
we're currently eyeballing 20% of these could be severe or critical, needing
92,800 hospital beds. In four weeks. Or hundreds of thousands, then millions of people die.
If we don't get a miracle, and the situation's numbers don't change abruptly.
- But think for yourself. Don't trust my numbers, don't trust anyone else's numbers.
Run the numbers for yourself, using your own calculator, and this table.
This epidemic is like a neutron bomb that wipes out people, but leaves buildings intact.
You need to assume that everyone outside is infected.
If you come close to someone else, or breathe their air, you might die.
Share this table with your friends and neighbors. Make sure they get it.
We're all in this together.
Don't Panic. Now that you understand what's actually going on,
it gives you power over the situation. It is what it is. Deal with it.
So, what are you going to do about it?
Be a proactive tiger who chooses your own destiny, not a reactive sheep.
Stay At Home and Stay Alive. Make Sure That We All Survive.
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