Some calculations on coronavirus infection risk

We want to know the probability of contracting coronavirus, especially from the viewpoint of someone for whom this poses a significant risk.  We try a top-down and a bottom-up approach.

Top down

The ONS gives an incidence rate of 0.04% per week over the course of their study (from 8 June to 21 June).  So the probability of not contracting CV in a week is (1- 5×10^-4)

The probability of not contracting CV in N weeks is (1- 4×10^-4)^N

The probability of contracting CV in N weeks is [1 – (1- 4×10^-4)^N]

So this gives results like:

Of course, we would not expect the incidence rate to stay stable in reality, and the probability of any individual becoming infected will depend on their own circumstances.  However, this does indicate that it would be highly desirable to attain a technical solution vaccine, etc to COVID-19 within 100 weeks/2 years.

Bottom-up

We start from contact between a susceptible and an infected person.

The prevalence of COVID is about 10^-3  ONS data 25 June.

The probability of infection given contact with an infected person is ~ 10^-1 [Suggested 5 x 10^-2 here]

• Prob of not being infected in 1 contact ~ (1-10^-4)
• Prob of not being infected in N contacts ~ (1-10^-4)^N
• Probability of being infected in N contacts ~[1- (1-10^-4)^N]

 

Or we can look at the lower range of this in more detail:

So this obviously raises a number of questions, such as:

i) what level of risk of infection is acceptable?

ii) what level of uncertainty is there in the parameter estimates?

iii)  what exactly is a contact?

What level of risk of infection is acceptable?

This is obviously not merely a question for individual judgement, give the possibility of transmitting infection directly or at many removes to vulnerable individuals.

Confining ourselves to the consideration of individual risk as a first step, we consider the case of a male in his early seventies without relevant underlying health conditions. Data from China gives an infection fatality rate of 4.3% for this group.  UK data shows something like a 2% risk for this group dying in a year.  So let us say our subject wants the risk of dying from COVID to be no more than one tenth of this normal risk.  So we require the risk of infection to be less than 0.05 in round terms, which means our subject should confine himself to about 500 qualifying contacts in a year at the current prevalence.

What level of uncertainty is there in the parameter estimates?

We can consider the question of who the contacts are.  On the one hand, you are more likely to have contact with a supermarket cashier than with a shelf-stacker, and cashiers are likely to have higher prevalence for that very reason—they are in contact with more people.  (Compare ONS treatment of US data.) On the other hand, it may well be that people with [relevant] symptoms have a higher prevalence than those without and are also likely to withdraw from contact. (0NS 12 June).  This could do with further and more systematic treatment.

What exactly is a contact?

This is of course a crucial question.  The latest official UK advice with regard to contact tracing as of 17 June says:

What do we mean by a ‘contact’?

A ‘contact’ is a person who has been close to someone who has tested positive for COVID-19 anytime from 2 days before the person was symptomatic up to 7 days from onset of symptoms (this is when they are infectious to others). For example, a contact can be:

people who spend significant time in the same household as a person who has tested positive for COVID-19

sexual partners

a person who has had face-to-face contact (within one metre), with someone who has tested positive for COVID-19, including:

being coughed on

having a face-to-face conversation within one metre

having skin-to-skin physical contact, or

contact within one metre for one minute or longer without face-to-face contact

a person who has been within 2 metres of someone who has tested positive for COVID-19 for more than 15 minutes

a person who has travelled in a small vehicle with someone who has tested positive for COVID-19 or in a large vehicle or plane near someone who has tested positive for COVID-19

Where an interaction between 2 people has taken place through a Perspex (or equivalent) screen, this would not be considered sufficient contact, provided that there has been no other contact such as any of those indicated above.

So we can take this as a characterisation of the qualifying contacts between two people which might lead to transmission of infection.

Or we can say that R₀ = (contacts per day)*(transmission probability per contact)*(number of days case is infective).

So we take R₀ as about 3, transmission probability per contact 0.1 and  infectious period 10 days, so

3 = (contacts per day)*(0.1)*(10)

So there are something like 3 qualifying contacts per day in a state of nature before imposition of social distancing, which implies a fairly substantial kind of contact.

Conclusions

On the basis of the discussion above, and indeed of common sense, we would say that if you are in a group where COVID-19 poses a significant risk, you should limit your qualifying contacts (with contacts as defined in the contact tracing guidance) as much as possible  unless or until this threatens to do tangible harm to yourself or others.

 

Are there any good Russian words in English?

That is a question I have often asked myself over the decades.  Russian words in English tend to fall into two categories:

i)  specifically Russian/Soviet referents:  tsar, rouble, Gulag, commissar, perestroika, glasnost, vodka, cosmonaut [Russian spaceman], sputnik [Russian satellite], samovar and so on

ii) terms with a negative connotation:  Gulag, commissar, ukase, pogrom, [actually maybe this is not a separate category].

So what might there be that is neither Russian nor pejorative?

It seems hard to derive bistro from быстро on chronological grounds, whatever the sign above might say.

The sable is tenné, not sable

Sable, as well as being an animal that lives in Russia and Poland is a highfalutin term for black as used by Shakespeare among others.  There are a lot more соболь in Russia than there are soból in Polish, but Poland is nearer.  Intelligentsia with that kind of spelling looks Russian rather than Polish (inteligencja) and the concept itself is just foreign rather than specifically Russian.

I quite like the word bolshie as a candidate here.  While it is clearly derived from Bolshevik (so Russian rather than Polish) it has no trace of Russianness attached to it and indeed has a semi-affectionate diminutive quality.  While the meaning of ‘difficult, recalcitrant, uncooperative’ may not seem especially positive, to the English mind these are not necessarily bad qualities–it may be different elsewhere, of course…

The book with no name

Well that was an enigmatic book arrived recently (no dustwrapper).

Maybe the idea was to boost sales by making Wurthwein’s ‘Text of the Hebrew Bible’ look like a discreet edition of ’50 Shades of Grey’.

One of a multivolume set of course, though 50 parts might be too much.

 

Or maybe it represents the ‘palimpsest’concept in a metaphorical kind of way…nihilistic even….

Joseph Henry Blackburne lived here

50 Sandrock Road

J. H. Blackburne dominated British chess during the second half of the 19th century, and at one point he was the world’s second most successful player.

He is perhaps best known for losing heavily to Wilhelm Steinitz and for taking it badly, but according to the biography by Tim Harding he was living in 9 Whitbread Road, Brockley at the time of the 1901 census, later moving to 45 Sandrock Road and then number 50 in the same road, where he died on 1 September 1924.

45 Sandrock Road

So number 45 has changed over the years more radically than number 50, but not as radically as the place in 9 Whitbread Road.

Presumed site of 9 Whitbread Road

Now then, it is known that Blackburne was bombed-out during a German raid in the First World War, but the dates are such that it’s unlikely the view above came into being that way.

J. H. Blackburne (1841-1924)

Now then Steinitz apparently lived in Shoreditch, which only adds to my suspicions that he was really Karl Marx on his day off…

How popular is Russia in the UK?

We are sometimes asked how popular Russia is among people in Britain.

In 2015, Chatham House reported results from surveys in 2012 and 2014 asking respondents which countries they felt especially favourable and unfavourable towards.   Above, we derive an overall favourability score from (favourable – unfacourable) , take the average of  this 2012 and 2014 and plot it against the change between the two dates.

We see that Russia is out on its own in terms of being unpopular and becoming more so, followed at a respectful distance by Israel.  This is presumably due to a series of notable events in this period: BP, Pussy Riot, Greenpeace, Ukraine, none of which were well received.

Interestingly enough, a BBC poll of about the same period of attitudes to different states in a sample of 22 countries showed Russia as among the least popular but without the same deterioration.

Stationary points of f(x)=x+√x

The curves in the pic are f(x) and f'(x).

Question: The function is f(x)=x+√x. Can you find its min or max value? If you calculate f'(x) and put it to 0, you get x=1/4. But draw the curve and there is no such max/min there.

One suggestion:   Clearly f'(x) has two asymptotes at x=0 and y=1 and so can never be 0 for any real value of x. But why does differentiating lead to the result x=1/4? I agree that f(x) = x-√x has a clear minimum there, but it’s a different function. My answer was that since there’s an infinity at x=0 f'(x) is undefined, but I’m not convinced that’s the answer.

OK, so √x is defined as the positive value of x^(1/2).

Let’s see if we can differentiate it:

x = √x√x  where x, √x >= 0.

D(x)  = 1 = 2√x*D(x) => D(x) = 1/(2√x)

So, f'(x) = 1 + 1/(2√x)

if f'(x) =0, then √x = -1/2.  But √x is >= 0 by definition, so there is no solution.

Let’s try to be a little more systematic while staying within the bounds of high school maths.

We consider the function  g(x,c) = x + x^(1/2)

where x^(1/2) = (√x)*(-1)^c

and we choose c to be either 0 or 1.

So g'(x) = 1 + (1/2√x)*(-1)^c

Setting g'(x) = 0 =>

√x = (-1/2)*(-1)^c

But since  √x is positive, c must be 1 rather than 0 for this to have a solution.

So by accepting a solution here we force the original function to be g(x) = x – √x.

 

Prometheus Bound, Greenwood Theatre 1430 8 February

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At the end:  chorus–Prometheus–Io

Prometheus Bound certainly made an interesting choice for this year’s KCL Greek Play in Greek.  One question is whether it actually is a play or merely a scene-setting for following parts of a trilogy.  Nothing much happens apart from various characters coming to sympathise with or talk sense into Prometheus and him referring to the injustices he has suffered and the dark secret he knows.

I remember a production at the Soho Theatre where the clientele were expected to be satisfied by a combination of the manly heaving of the hero’s bare breast and chains.  Lots of chains.  But here it wasn’t quite like that.  We had a female Prometheus, and Oceanus, and whichever it is of Force and Violence that doesn’t actually say anything.

More generally, I’m afraid that there was no sign of a solution to the severe problems posed by staging this piece.  It started off with projections of various modern figures, especially Donald Trump, and you could see how Prometheus might be a kind of Nelson Mandela in captivity, but his captors needed him more than he needed them.  Or Trotsky perhaps, who thought he had the earth-shaking prophecy and was a prisoner to his own well-founded fears. But nothing came of this possible line of thought.

Rather than being chained to a cliff with a wedge through her chest, our Prometheus had to top of a table to call her own.  For some reason sound effects and lianas suggested that this was in the jungle somewhere.  Loud sound effects meant you couldn’t hear what was being said, though the Greek verse sounded to be spoken competently enough.  At the end, Prometheus’s final defiance got lost in underwhelming stroboscopic effects..

On the positive side, the entrance of the chorus was effective, as were some of their choreographed moves.  Likewise for Io’s entry and exit, though I’m afraid she did rather remind me of the domovoy from Morphine.  And indeed there were similar surtitling issues, with lots of text appearing some time after the event.

If you ask what I would have done–well, have a much larger chorus and have them sing and dance.  In fact, have them on stage the whole time and have them  hold up the surtitles on placards, to give the idea of a debate of some importance not people  coming on stage and exchanging words about mouldy mythology…But making something out of Prometheus Bound would be difficult with the best performers and technical resources in the world…

 

 

 

 

 

Morphine, Etcetera Theatre 7 February

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Picture from Anna Denshina’s Twitter feed

So let’s think–what problems might there be with staging Bulgakov’s ‘Morphine’, about a country doctor who falls victim to…err…morphine? Well, putting a non-dramatic work on the stage is always problematic–if the author had wanted to write a play he’d have done things differently. And especially in a case like the present, where the original text is in the first person and reflects the hero’s diseased apprehension of reality more than actual happenings between people. The latter is where you need to have things in a play. Here we also have some more objective narration from ‘Notes of a young doctor’ brought in to set the scene as well.

That said, the show combined the Russian tradition of having music in lots of places where you don’t want it with the English one of having characters shuffle on, deliver their lines through a mask of embarrassment, and then shuffle of again. The cast members showed various levels of comfort with appearing on stage and the Russian language…that said, I thought that Anna Danshina put in a good and affecting performance as the love interest called Anna.

There were also sutitling issues–the surtitles contained a lot of text at one go and tended to catch up after the event.  But I suspect the proportion of the audience who neither knew Russian nor the storyline of ‘Morphine’ was rather small…

Daily Mail: Enemies of the People

She’s quite right of course–‘Enemies of the People’ in English is either calqued from Russian or a translation of Ibsen’s En folkefiende.  There is ‘public enemy’ in English but that means something rather different. In French Revolutionary parlance,  ennemi du peuple is (or was) possible, but rather less likely than ennemi public.  I  don’t even know what народный враг would mean in Russian, since народный is strictly positive in its connotations…

‘And the Lord said…’ (Boris Khersonsky)

And the Lord said:  Katsap, where is Khokhol thy brother?
And Katsap answered: I am not his keeper Lord
And the Lord said: You sat to eat together
You sang his songs, you put him to the sword!

And Katsap said: Khokhol is himself at fault,
He is a traitor, greedy, he nibbled all the fruit,
He has artillery in the yard and a gun in the vault
And he puts my first-born right into dispute.

And the Lord said: Not first-born, but born to hate!
Forgetting, Katsap, that the Lord is father to you.
For I will say to Peter, who stands at Heaven’s gate
I will say to Peter, not to open to you.

And the Lord said: Turk, where is thy brother, Khach?
And the Turk answered: Am I his keeper, Lord?
And the Lord said: You thought I would not catch
Weeping from the ground, would not hear, not reward.

And the Lord said: Kraut, where is thy brother, Yid?
And Kraut said, I am not his keeper, nay.
And the Lord said: His blood is yelling what you did,
For vengeance is mine, and I will repay.

И сказал Господь: “Кацап, где брат твой, Хохол?”
Ответил Кацап: “Не знаю, я не сторож Хохлу!”
И сказал Господь: “Ты с ним садился за стол,
ты пел его песни и ты толкаешь его во мглу!”

И ответил Кацап: “Хохол – он сам виноват.
Он – предатель, он жадина, он яблоки все надкусил,
у него в огороде пушка, а в шкафу автомат,
он старшему брату, мне, противится что есть сил!”

И сказал Господь: “Ты не старший, ты страшный брат!
Ты забыл, Кацап, что Отец твой – Бог.
Вот скажу Петру, что стоит возле райских врат,
вот скажу Петру, он не пустит тебя на порог.

И сказал Господь: “Турок, где брат твой, Хач?”
И ответил турок “Не знаю! Я не сторож Хачу!”.
И сказал Господь: “От земли возносится плач!
Ты думал, что я не услышу, что я смолчу?”

И сказал Господь: “Фриц, где же брат твой, Жид?”.
И ответил Фриц: “Не знаю, я не сторож Жидам!”
И сказал Господь “Кровь Жида за тебя говорит.
Ибо Мое есть отмщение и Аз воздам.”