The Power of Social Distancing - Explained By Folding Paper
26 Mar 20
Inzpire
I may have pursued a career in Physics had the lure
of aviation not drawn me away. Nonetheless, Maths and Physics have always
interested me.
The events of the past few weeks rekindled that interest as I watched the numbers of people infected with SARS-CoV-2 (the virus that causes Covid-19) doubling every few days. I got to thinking about the underlying maths and remembered something that a physics lecturer had once told me about the power of doubling.....
Over the past weeks we have all learned that epidemiologists use the term Ro (R naught) to describe the average number of other people an infected person infects.
Most of them seem to think that the Ro for SARS-CoV-2
(the virus that causes C-19) is somewhere between 1.5 and 3.5.
For simplicity, let’s assume that Ro is 2, which is at
the lower end of the above range. This means that, on average one person
infects 2 others.
To illustrate the dramatic effect of this, consider
the everyday act of folding an imaginary piece of paper, thus doubling its
thickness.
Let’s imagine the paper is 1/10 of a millimetre thick
and infinitely wide (so that we can just keep folding it for ever).
After 1 fold, it is 1/5th of a millimetre
thick
At the third folding, it is as thick as a thin piece
of card.
By the 7th folding, it is as thick as book
By the 10th folding, it is as wide as your fist.
At the 23rd folding, it is 1 kilometre wide.
At the 30th folding, it will be 100 kilometres wide.
42 folds will make it as thick as the distance from
the earth to the moon.
After 51 folds, it will be as thick as the distance from
the earth to the sun.
By the 81st fold, the paper will be 127,786 light
years thick. This is almost equal to the diameter of the Andromeda Galaxy
(which is about 141,000 light-years).
By the 90th fold,
the pile of paper will be 130.8 million light-years thick, which is more than a
Virgo supercluster of galaxies (which includes the Andromeda galaxy, our own
Milky Way, and about a hundred other galaxies).
Finally, after 103
folds, the original 0.1mm Piece of paper is thicker than the observable
universe, with a diameter of 93 billion light years.
103 folds to become bigger than the observable
universe! That’s the power of simple doubling.
Now, back to
SARs-CoV-2 and C-19. Doubling is happening every few days.
There is a strong parallel between a piece of paper being folded in half and a single C-19 patient infecting two others. They are effectively the same thing.
It is no surprise that these graphs looks similar
shapes!
This is why it is so
important for everyone at to obey Government advice. At Inzpire we have
been enacting social distancing for 10 days with all of our staff working from
home since Tuesday 17 March. We have distanced ourselves before the numbers get
even bigger.
Actually, the Ro of
SARS-CoV-2 is believed to be closer to 2.5 not 2. So a single person infects
more than 2 others, and this makes C-19 expand even faster than the folded
paper example above. Sobering.
On the positive
side, if a combination of social distancing, immunity or perhaps, in time,
immunisation, bring down Ro, then the effects at the tail end will be dramatic.
This is what the Government is trying to do.
If Ro can be
reduced to less than 1, on a global scale, then the disease would eventually die
out because, on average, an infectious person will transmit to fewer than one
other susceptible person. That is what happened with Smallpox, which has now
been eradicated.
For the moment,
though, the emphasis is on reducing the rate of climb of the graph to keep the
numbers manageable. We can all play our part.
Yes, this is a serious
situation but by obeying Government advice and doing all the things that we are
being asked to, there can be a big effect; China has shown that this can happen.
C-19 cases in China have fallen rapidly due to the actions they have taken.
So, stay at home where
possible (unless you are a key worker), avoid as many people as you can, comply
with the Government advice, wash your hands (a lot!), look after each other and
stay positive. This will end.
Here at Inzpire, we
will be practicing all of the above whilst doing everything we possibly can to
keep delivering an excellent service to all of our customers. For the
foreseeable future during the pandemic, our priorities will be:
1. The safety of our employees and their
families
2. Delivering the highest quality service for
our amazing customers
3. Sustaining our business for when this
is all over.
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