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Exponential growth is difficult to understand. There are several strange features which don't 'feel right'. It can lead to misunderstanding, and as a pandemic follows exponential growth, it helps to consider how it works.
A thread.
1/12
A thread.
1/12
All exponential growth is worked out by multiplying the number of cases by a number. In this pandemic, we have been calling this the R number.
If we start with 16 cases and have an R of 0.5, the cases will follow the pattern:
16 x 0.5 = 8
8 x 0.5 = 4
4 x 0.5 = 2
2 x 0.5 = 1
2/12
If we start with 16 cases and have an R of 0.5, the cases will follow the pattern:
16 x 0.5 = 8
8 x 0.5 = 4
4 x 0.5 = 2
2 x 0.5 = 1
2/12
With an R of less than 1, the cases will go down and eventually stop. If we use an R value of 1, we get:
16 x 1 = 16
16 x 1 = 16
and so on, It never gets worse, but it never gets better either.
3/12
16 x 1 = 16
16 x 1 = 16
and so on, It never gets worse, but it never gets better either.
3/12
What if R is 2?
16 x 2 = 32
32 x 2 = 64
64 x 2 = 128
Cases will keep doubling.
In any exponential growth, if R is greater than 1, the number of cases will eventually double, then double again. All that changes is the time it takes for them to double.
4/12
16 x 2 = 32
32 x 2 = 64
64 x 2 = 128
Cases will keep doubling.
In any exponential growth, if R is greater than 1, the number of cases will eventually double, then double again. All that changes is the time it takes for them to double.
4/12
Assume you have a hospital which has a maximum capacity for 512 patients at any one time. Let's start with 1 patient in January and keep doubling every month.
How long will it take for the hospital to be full?
5/12
How long will it take for the hospital to be full?
5/12
January 1
February 1 x 2 = 2
March 2 x 2 = 4
April 4 x 2 = 8
May 8 x 2 = 16
June 16 x 2 = 32
July 32 x 2 = 64
August 64 x 2 = 128
September 128 x 2 = 256
October 256 x 2 = 512
So In October we have a problem.
6/12
February 1 x 2 = 2
March 2 x 2 = 4
April 4 x 2 = 8
May 8 x 2 = 16
June 16 x 2 = 32
July 32 x 2 = 64
August 64 x 2 = 128
September 128 x 2 = 256
October 256 x 2 = 512
So In October we have a problem.
6/12
By November we have a disaster.
November 512 x 2 = 1024
By December a catastrophe.
December 1024 x 2 = 4096
But at what point was the hospital half full?
7/12
November 512 x 2 = 1024
By December a catastrophe.
December 1024 x 2 = 4096
But at what point was the hospital half full?
7/12
In September, just one month before the hospital was full, it was only half full.
When did the hospital have 90% capacity?
8/12
When did the hospital have 90% capacity?
8/12
Sometime in June / July, 4 months before it was overwhelmed, the hospital was 90% empty.
If someone at this time suggested locking down to protect the hospital, it would seem strange and people might argue it wasn't needed because the hospital was virtually empty.
9/12
If someone at this time suggested locking down to protect the hospital, it would seem strange and people might argue it wasn't needed because the hospital was virtually empty.
9/12
The rise in cases determined by any R value greater than 1 will have the same effect. Just before the hospital is overwhelmed, everything looks like it's fine.
And then it isn't and soon thousands of people can't access the hospital and are left on their own to die.
10/12
And then it isn't and soon thousands of people can't access the hospital and are left on their own to die.
10/12
Of course in a real situation, hospital space becomes available, either through recovery or deaths.
This has an impact but the exponential growth still follows the pattern above.
Reducing the R *and* allowing hospitals time to deal with the patients they have will help.
11/12
This has an impact but the exponential growth still follows the pattern above.
Reducing the R *and* allowing hospitals time to deal with the patients they have will help.
11/12
This is where lockdowns do help. They reduce the R number meaning the cases grow more slowly, giving hospitals time to treat the patients they have and allow them to free up more beds than they lose to new admissions.
12/12
12/12
