# Numbers Don\\\'t Lie...

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In article <rcvl5f\$rko\$1@gioia.aioe.org>,
Martin Brown <\'\'\'newspam\'\'\'@nezumi.demon.co.uk> wrote:
<SNIP>
At the present burn rate the USA will have the infection rampant for
several years or until an effective vaccine is developed. Either way the
limiting factor will be herd immunity lowering the effective R value.
I looked a long time at this sentence to find out what was intuitively wrong.

The correct way to express this is
\"
Either way the limiting factor will be that sufficient people are immune
lowering the effective R value to under 1.
Then we have reached herd immunity which is by definition that
for the population at large R is under 1.
\"
You are excused somewhat because herd immunity is misnomer.
The herd is not immune to the disease, the herd is no longer susceptible
to an epidemic. I call it herd-immunity, to stress that it is
a word combination that has a specific meaning like flying-fox
(which is a bat not a fox).
\"
Having a single number for the whole population is simplistic.
You could for example have a population that is divided in two
cohorts (lets name them red and blue, pun intended) where the
red\'s have a higher R value and a larger part that is immune,
the blue\'s have a lower R value and a lesser part that is immune.
The effective R will be between the two. The blues would be much
better off without the red\'s.

The herd-immunity figure can be calculated with a single R model
and perfect mixing of the population, meaning that the chance
of being infected by any other specimen of the population
is equally likely. (This is not at all unreasonable... for
a herd.)
Now we arrive at a model with N cattle and I infected:
I\' = (N-I)R
This dies out with the result that every cattle is infected.
Now we could have a headstart, replacing N by N-I_0.
This also dies out, but now not all the non-immune cattle is
infected. (Hurrah!).
I never before thought herd-immunity through because it is
so absurd as a policy, but once you do it is clear that
the level of immunity required is very much dependant on R.
In other words if you want to reach herd-immunity earlier,
with a less death toll, wear masks, keep social distance, avoid gathering.
And keep doing that for eternity.

It stresses again the absurdity of herd immunity through infection.
The only viable options are:
1. exterminate through isolation and tracing (china, vietnam, korea, taiwan)
2. vaccination (USA UK EU)

--
Regards,
Martin Brown
Groetjes Albert
--
This is the first day of the end of your life.
It may not kill you, but it does make your weaker.
If you can\'t beat them, too bad.
albert@spe&ar&c.xs4all.nl &=n http://home.hccnet.nl/a.w.m.van.der.horst

M

#### Martin Brown

##### Guest
On 19/11/2020 12:16, albert wrote:
In article <rcvl5f\$rko\$1@gioia.aioe.org>,
Martin Brown <\'\'\'newspam\'\'\'@nezumi.demon.co.uk> wrote:
SNIP
At the present burn rate the USA will have the infection rampant for
several years or until an effective vaccine is developed. Either way the
limiting factor will be herd immunity lowering the effective R value.

I looked a long time at this sentence to find out what was intuitively wrong.

The correct way to express this is
\"
Either way the limiting factor will be that sufficient people are immune
lowering the effective R value to under 1.
Then we have reached herd immunity which is by definition that
for the population at large R is under 1.
\"
You are excused somewhat because herd immunity is misnomer.
The herd is not immune to the disease, the herd is no longer susceptible
to an epidemic. I call it herd-immunity, to stress that it is
a word combination that has a specific meaning like flying-fox
(which is a bat not a fox).
\"
Having a single number for the whole population is simplistic.
Oh I agree whole heartedly. *FAR TOO SIMPLISTIC*. The average \"R\" number
is a complete crock of shit that politicians think they understand.

You could for example have a population that is divided in two
cohorts (lets name them red and blue, pun intended) where the
red\'s have a higher R value and a larger part that is immune,
the blue\'s have a lower R value and a lesser part that is immune.
The effective R will be between the two. The blues would be much
better off without the red\'s.
The actual model I used to analyse it was a binary split of populations
with two R values Rlow for the general population and Rhigh for key
workers and healthcare professionals on the front line. This bimodal
model is close enough to model most of the behaviours. In reality the
probable value of R is a continuous function p(R) on 0...1000 or so.

I am ignoring the cross talk between the two populations.

Here is the analysis for the simplest bimodal case where for a concrete
example I chose to make average R=0.7 and the fractions f,1-f. Orginally
posted in a similar discussion in ulm 28/9. New Google gropes is rubbish

The simplest realistic model of Covid partitions the population into two
risk groups. Public fraction f and high risk medics/key workers (1-f).

We can construct their respective R values from the average R as follows
by introducing an unknown x which we can vary within certain limits.

Group Fraction R_effective

Public f R-x/f
Medic 1-f R+x/(1-f)

Average R f(R-x/f)+(1-f)(R+x/(1-f)) = R-x+x = R

x can vary from 0 through to R*f (R cannot be negative). And we can
choose any value we like for x in that continuous range so that there
are already an infinite number of possible solutions with the right
average R in this very simplest of bimodal toy pandemic models.

x=0 represents the simplest possible Noddy uniform world case.

Typical values for f = 29/30 (~97% chosen to make sums easier).

What we actually saw at the beginning of the pandemic was a situation
where the medics and key workers were still being hammered long after
the general population were benefiting from a much reduced R. We can ask
the reasonable question what value might x have been in early lockdown.

Pessimistic x=0.1 R_low = 0.6 R_high = 3.7
Optimistic x=0.05 R_low = 0.65 R_high = 2.2
Limit case x=0.01 R_low = 0.69 R_high = 1.0

The crucial point here is that in an important subset of the population
infections are still rising exponentially even though average R is well
below one. This is basically what happened in care homes and hospitals.

The case doubling/halving time is always well defined but the average R
number is subject to a large number of hidden and subjective
assumptions. Working it out from the observed data is fraught with
difficulties. It is an ill posed inverse problem with bells on.

The herd-immunity figure can be calculated with a single R model
and perfect mixing of the population, meaning that the chance
of being infected by any other specimen of the population
is equally likely. (This is not at all unreasonable... for
a herd.)
Now we arrive at a model with N cattle and I infected:
I\' = (N-I)R
This dies out with the result that every cattle is infected.
Now we could have a headstart, replacing N by N-I_0.
This also dies out, but now not all the non-immune cattle is
infected. (Hurrah!).
I never before thought herd-immunity through because it is
so absurd as a policy, but once you do it is clear that
the level of immunity required is very much dependant on R.
In other words if you want to reach herd-immunity earlier,
with a less death toll, wear masks, keep social distance, avoid gathering.
And keep doing that for eternity.

It stresses again the absurdity of herd immunity through infection.
The only viable options are:
1. exterminate through isolation and tracing (china, vietnam, korea, taiwan)
2. vaccination (USA UK EU)
Herd immunity acquired by vaccination is not significantly different in
principle from herd immunity acquired by catching the disease. That is
precisely how well control the childhood diseases like Polio and MMR.

It is just vaccination much less likely to kill you than the disease.

--
Regards,
Martin Brown

T

#### Tom Gardner

##### Guest
On 30/11/20 13:00, Bill Sloman wrote:
On Monday, November 30, 2020 at 8:39:21 PM UTC+11, Martin Brown wrote:

The urban poor on the breadline cannot afford to be off sick so they go to
work anyway thus spreading the disease. Some even work in factories where
social distancing is all but impossible and for unscrupulous employers who
don\'t really care either.

This is plausible - to some extent - but sounds more like propaganda than
anything evidence-based.
There\'s always that danger, but there have been some disquieting
revelations.

Meat processing plants, here and in the US, have seemed to be a
problem w.r.t. spreading disease - but that could be the PETA
processing is similar; if not, why not?

There does seem to be a few outbreaks associated with supermarket
workers, and my inside data points indicate the industry definitely
tries to keep specific information under wraps.

Most notoriously, the rag trade in Leicester was found to be
rife with illegal working conditions and illegally low hourly
wages.

B

#### Bill Sloman

##### Guest
On Tuesday, December 1, 2020 at 2:08:07 AM UTC+11, Tom Gardner wrote:
On 30/11/20 13:00, Bill Sloman wrote:
On Monday, November 30, 2020 at 8:39:21 PM UTC+11, Martin Brown wrote:

The urban poor on the breadline cannot afford to be off sick so they go to
work anyway thus spreading the disease. Some even work in factories where
social distancing is all but impossible and for unscrupulous employers who
don\'t really care either.

This is plausible - to some extent - but sounds more like propaganda than
anything evidence-based.

There\'s always that danger, but there have been some disquieting
revelations.

Meat processing plants, here and in the US, have seemed to be a
problem w.r.t. spreading disease - but that could be the PETA
It\'s been a problem in Australia as well. The people chopping up the meat seems to stand fairly close together, and the air conditioning is set to keep the meat fresh rather than the processing staff healthy.

> I\'m not sure whether other food processing is similar; if not, why not?

Meat comes in bigger chunks, and goes off faster. Seafood processing doesn\'t seem to produce the same problems - at least not since the Wuhan wet market, and that may have been due to under-the-counter trade in wild-animal meat (with pangolins as the prime suspect).

There do seem to be a few outbreaks associated with supermarket
workers, and my inside data points indicate the industry definitely
tries to keep specific information under wraps.
Australian supermarkets spaced out their cash registers and insisted on 1.5 metre spacing between people in queues. Most of them insisted that their customers wore masks.

> Most notoriously, the rag trade in Leicester was found to be rife with illegal working conditions and illegally low hourly wages.

If it had been well enough known to be evidence, the police would have moved in. If you don\'t know about it. you can\'t figure it into your model.

--
Bill Sloman, Sydney