Keep your Bubble small
Double your Bubble
Score will redouble
Twice would be nice
Four times not thrice
You’re in more trouble
18 April 2020
The New Zealand Government will decide on Monday whether (two days later) we will stay at Lockdown Level 4 or go down to Level 3.
Regardless of the decision on Monday, the risk of contracting COVID-19 will still exist and will be increased if we go down to Level 3.
Level 3 will allow Bubbles to increase in size.
In this post we will look at the risk of increasing the size of your Bubble.
You may consider your Bubble as being a circle.
There are a number of Bubbles (circles) in the image below:
It is assumed that the circumference of each circle has a boundary 1 metre wide so that all people in one bubble are at least 2 metres away from people in a nearby bubble.
We will consider the increased risk factor/score if you increase the size of your bubble.
If you double the size (radius or diameter) of a circle (or a square) the area of the new circle will be four times the original circle (or square).
Suppose two people in their own individual Bubbles make a new Bubble together.
The risk when they make the new Bubble must be greater than that for each of the old Bubbles (added together).
It makes sense to assume that the radius of the new Bubble (circle) is twice the radius (1) of the old Bubbles.
Hence the area of the new Bubble is 4 (=4/1) times the area of each of the old Bubbles. i.e. the area of the new Bubble is twice the sum of the two old Bubbles.
We extend this and get the formula for the [increased] risk factor (F) calculated using the formula
(new group size)^2
(old group size)^2
where the new group size is the sum of the size of the old groups.
The factor F is the ratio of the relative size of the circles.
This gives us the following table for calculating the (increased) risk factor (F) :
|Old Group||Add Group of size|
For example if 2 people join a group of 5 people, then the [increased] risk factor for the group of 5 people (bottom line of the table) is
which is 1.96 (=49/25). i.e. the risk is almost double what it was originally for the old group of 5.
If 5 people join a group of 2 people the [increased] risk factor (for the 2 people) is
which is 12.25 (=49/4).
This assumes the 2 people were already in their own group.
If they were in their own individual bubbles previously, then we need to multiply the risk factor by 4 (=4/1) to get a risk factor of 50 (=4 x 12.5) for the people in their own individual bubbles if they join a group of 5 people.
Assume two groups are of equal size (with n people in each group).
Let Gn be the original risk factor for a group of n people.
When the two groups combine into a single large group (of size 2n),
the [increased] risk factor is 4 (see the diagonal in the table).
Thus the increased risk factor for the new group twice the size (2n) is
= 2Gn + 2Gn
=2(Gn + Gn)
i.e. The new risk factor is double the risk factor for two groups half the size of the new group. We consider two groups so that we have a total of 2n people before and after the calculation.
In addition the original bubbles may stay in their own geographic area and there may be different spread of COVID-19 in each of these. The increased risk is shared with the new bubble.
The lessening of other restrictions at Level 3 will further increase the risks.
Stay in your own Bubble!
Note: The above is my own theory (developed today) which may or may not be correct but appears to be consistent.
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