COVID-19 NZ: We are down to Level 3 Lockdown. Keep your Bubble exclusive and small!

Threedom

The Herald calls L3 Threedom
This seems more cheesy than edam
Please keep your Bubble small
For no virus at all
Hope L2 gives us more freedom

Alan Grace
28 April 2020

 

Keep your Bubble small

Double your Bubble
Score will redouble
Twice would be nice
Four times not thrice
You’re in more trouble

Alan Grace
18 April 2020

Keep your Bubble exclusive and small!

We again look at the increased risk if you extend your Bubble.
We extend the work done in a previous post:
https://aaamazingphoenix.wordpress.com/2020/04/18/covid-19-what-is-the-risk-of-extending-your-bubble-stay-in-your-own-bubble/

We looked at this table:

Group		Add People		(n+m)^2/n^2
Size	1	2	3	4	5
1	4.00	9.00	16.00	25.00	36.00
2	2.25	4.00	6.25	9.00	12.25
3	1.78	2.78	4.00	5.44	7.11
4	1.56	2.25	3.06	4.00	5.06
5	1.44	1.96	2.56	3.24	4.00

The values are arbitrary. They are indicative only. However lease see criterion 4 below.

We will also consider this table:

Group		Add People		2(n+m)/n
Size	1	2	3	4	5
1	4.00	6.00	8.00	10.00	12.00
2	3.00	4.00	5.00	6.00	7.00
3	2.67	3.33	4.00	4.67	5.33
4	2.50	3.00	3.50	4.00	4.50
5	2.40	2.80	3.20	3.60	4.00

Either of the above tables would be suitable for showing the increased risk if you extend your Bubble.

Which table do you  prefer?

Intuitively the risk of adding one person (in isolation by himself/herself)) to a group is significantly more for the individual than if is for the group.

We will use R(a,b) to indicate the increased risk of adding a Bubble with b people to a Bubble with a people. The above tables show possible values for R(a,b).

We could use any table which meets the following criteria:

1. If a Bubble is doubled in size (say n=2m), the new Bubble will have a risk factor twice  the size of two groups the same size as the original. This means R(n,n) = 4.
   i.e. The value 4 is along the [leading] diagonal.
2. If b>a then R(a,b)>R(a,a) and R(b,a)<R(b,b).
   This means R(a,b)>4 and R(b,a)<4.
   This means R(a,b)>R(b,a).
3. If b>a and c>b then R(a,c)>R(a,b) and R(c,a)<R(b,a)
   (look at the table and choose values for a, b, and c).
   i.e. Values in rows increase and values in columns decrease.
4. R(a,b)> (a+b)/a
   i.e. The values in the table should be greater than these values:

Factor =	1
Group		Add People
Size	1	2	3	4	5
1	2.00	3.00	4.00	5.00	6.00
2	1.50	2.00	2.50	3.00	3.50
3	1.33	1.67	2.00	2.33	2.67
4	1.25	1.50	1.75	2.00	2.25
5	1.20	1.40	1.60	1.80	2.00

The original table was developed by considering the ratio when circles are increased in size. If the diameter (or radius) of a circle (or square) is increased the new area is in proportion to the square of the ratio of the radius.

For example, if the size (radius) is doubled (x2), the area is 4 times the original circle.

Feedback suggested a linear (straight line) model could be suitable. See table 2.

A combination of the above tables would also work.

The table below uses the values from one table above the diagonal and the other table below.

This may possibly be better:

Group		Add People		Combo
Size	1	2	3	4	5
1	4.00	6.00	8.00	10.00	12.00
2	2.25	4.00	5.00	6.00	7.00
3	1.78	2.78	4.00	4.67	5.33
4	1.56	2.25	3.06	4.00	4.50
5	1.44	1.96	2.56	3.24	4.00

The values in any table could be adjusted (e.g. rounded or truncated) if desired so long as the criteria are still being met.

The values in a table (check criterion 4) should not be much smaller than:

Factor =	1.25
Group		Add People
Size	1	2	3	4	5
1	2.50	3.75	5.00	6.25	7.50
2	1.88	2.50	3.13	3.75	4.38
3	1.67	2.08	2.50	2.92	3.33
4	1.56	1.88	2.19	2.50	2.81
5	1.50	1.75	2.00	2.25	2.50

Note: the above values are only 25% above (x 1.25 above) the minimum limit set in criterion 4.

I recommend values not smaller than:

Factor =	1.2
Group		Add People
Size	1	2	3	4	5
1	2.40	3.60	4.80	6.00	7.20
2	1.80	2.40	3.00	3.60	4.20
3	1.60	2.00	2.40	2.80	3.20
4	1.50	1.80	2.10	2.40	2.70
5	1.44	1.68	1.92	2.16	2.40

Note: the above values are only 20% above (x 1.2 above) the minimum limit set in criterion 4.

Which table do you prefer?

My other COVID-19 posts can be found here:
https://aaamazingphoenix.wordpress.com/tag/coronavirus/

Data for my posts can be found at:
https://www.worldometers.info/coronavirus/
https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_New_Zealand

I share my posts at:
https://guestdailyposts.wordpress.com/guest-pingbacks/