The Chances Of Meeting An Infected Person...

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BilSuth | 23:59 Sat 04th Apr 2020 | Science
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depend on the percentage out there, and how many you meet. The fewer the better, obviously. I'm not talking about the chances of getting infected because distancing, maybe masks and other protections affect that calculation.
Not many people actually believe that if you throw dice six times, any given number is "certain" to come up. In fact, the chances of it NOT coming up are 5/6 to the power 6 or .33489. So the chances of success are .66511, roughly 2 out of 3.
It's a long time since I did calculus, stats and anything else related but I know that the formula for this would be (n-1)/n to the power n. This formula reveals that the higher value of n, the closer we get to .367879 or thereabouts (I've tried it to some high values e.g. 1million). That of course is the NON-event decimal; we have to deduct it from 1 to get our "success" answer, i.e. .632121 ... approximately.
Maybe one of you scholars out there can remind me about iterations, attractive fixed points, or whatever kind of sequence defines this formula.
Meantime, keep the odds down and stay safe, folks. One infected person can be one too many.


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the impasse ( whats that and was there one?) in theoretcial phys in the thirties was said to be the people involved werent able to communicate what they had done to others in the field....

so now they have to do history of maff modules because as I said to my dear nephew at Cambridge ( yeah maff) ; " you can go froo three years at university and not write a sentence in English".
he looked at me sharply
PP yes, before you can share ideas, there needs to be a common vocabulary and assumptions.
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Thanks to all for posts so far.
Peter P, I will scrutinise your answers relating to probability. Thanks.
Mozz71, don't worry -- a lot of this is academic, in any sense.
Two points about the real infections/deaths stats, although I'm not trying to second-guess the experts, just to pass on some tips I have read. First, you can't divide the current aggregate infections by the total deaths, because the latter run maybe a week behind. You need to see what the infections figure was (say) seven days previously because that's when the people who have died were infected. Sadly, that gives you a higher fatality rate in a scenario where infections continue to rise -- except perhaps in the case of South Korea, where figures have stabilised and the deaths remain around 2% by any calculation.
Secondly, graphs and newly introduced measures: You can see how various models work by plotting your own graph. If you project the current rising graph of infections into the future, say three weeks ahead, the dotted line of theoretical figures arrives at a certain point. If you flatten out the graph from today so that it is a straight horizontal line (as if the restrictions -- somehow -- had an immediate effect), you form a triangle with your artificial line as the base.
Without getting into calculations (height x width divided by two because it's a triangle and not a rectangle), the shaded area would represent the infections avoided (and consequently a saving in lives) which the restrictions are hoped to achieve.
Whether you're maths-minded or not, and agree with me or not, we all want to see those infection rates falling as soon as possible.
I was thinking of random walks - which is what you would be doing if you go out and randomly meeting someone
I am not sure why one of the postgrads was moved to comment - "what dat den?" Very AB but not very helpful

you tube has a lot on stochastic processes - just plug that in a search bar - they are pretty turgid - MIT coursesas

and they also go into Brownian motion - which to my mind is very near to what you want . The answer to the question "what is the chance a mol with meet a mol with energy greater than x " is directly applicable to what is the chance of meeting some who is infected if the infected rate is x
but that is me - the ideas may not be related to other people
the lectures are pretty turgid - but you are locked in
// You need to see what the infections figure was (say) seven days previously because that's when the people who have died were infected//

yeah but everyone thinks this is a big deal - but it is just looking at the graph but seven big squares to your left ( towards the x axis) because a big square represents one day

The thing about your graph idea is that if you have straight lines in this case when they start off with exponent
then you have transformed your axes ( log transform )

so now the area under the curve is triangular and IS related to the area under the curve of an exponent
the relation is froo something called a Jacobian
which is a bit eeky to manipulate
and you would be better off just getting a computer to count the squares beneath the untransformed curve

[the area under the curve estimation are done for blood flow estimations and drug distributions] - same maff different assumptions
// Sadly, that gives you a higher fatality rate in a scenario where infections continue to rise//

yeah agreed - but rather than say - "oh it is wrong let us chuck it out", it more sensible to say "if is an overestimate then it is an upper bound and an figures generated using it we know will be greater than those we can expect ....."

instead the statisticians and modellers heads are going pop like it is a scene from Scanners

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Agree with most of that, Peter. I am sure the "experts" would rather err on the side of safety. Everyone will be too relieved, whenever that time comes, to rebuke them for scare-mongering.
They have also trotted out that an infected person passes it on to an average 2.5 people. Presumably that is over the course of their infection. We don't know how many folk they had contact with but didn't infect. And how do they know? Numbers quickly got too high in UK to do thorough contact-tracing, unless they did it on a sample basis.
Not as easy as it looks ... S Korea, the flagship country as a model of effective response, has extensive testing including drive-ins and have done a lot of contact-tracing. This includes a phone app that gives text alerts when an infected person is nearby (which is why they can still have cafes/shops open) but the downside is civil liberty issues plus victimisation of infected people. But ... how do they know? Are the infected folk tagged? Why are they not confined to home or hospital?
Using the assumed seven-day lag between known cases and deaths, the picture on numbers we have is scary, but it becomes frightening if we were to say the lag could be up to 14 days, which could well be nearer the truth. Here in Spain the known infections number around 130,000 and the number of deaths around 12,400, meaning roughly one in eleven of the known cases has died. The number of known infections a week ago was around 80,000, which would give a figure of around one in six. Two weeks ago, there were only 30,000 known infections and that would mean that more than one in three of them has died!

We all realise that the number of infections must be far greater than the number of known infections, and factor that in, but we have to be careful which numbers we start with.
// nd factor that in, but we have to be careful which numbers we start with.//

yeah that is why we should IMO start with Deaths because it is so hard to hide a dead body. also I dont see why - +ve test and Hospital = infected case and anything else isnt
two Checkable and objective measures

I agree, PP, the only reliable number is deaths. However, some are trying to put deaths against some other figure, one we don't have, to get a percentage.
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Hi NickorWan, Spain sadly has the world's highest % of confirmed cases based on population, currently about 2,800 per million. That puts the known figure at 1 in every 300 but we known it must be higher -- everyone's is higher than that in reality.
The infections graph seems less steep and I know, as you say, it depends on your starting point. One of the links from below suggests 7 days is commonly used, probably because those who do succumb usually do so quite quickly. So maybe that helps a little. Meanwhile, you stay safe over there.
See also the thread after this one for a discussion about cases v. confirmed cases.
For example, PP, in the paper by Dr Lee posted the other day, he wrote that the number of infected cases could be 10 to 20 times that reported He then gave the known cases now divided by deaths and said that should be be multiplied by 10 to 20 , but of course it was the wrong starting point. He should have used deaths now and infected cases 7 – 14 days previously multiplied by 10 – 20 - a very different figure.

Thanks, Bilsuth, you stay safe too. I read that most die between day 18 and day 21, but I don't know where I read that.
Sorry, PP, a senior moment, I should have said...

He then gave the known cases now, and said that should be be multiplied by 10 to 20 before being divided by deaths, but of course it was the wrong starting point. He should have used known cases 7 – 14 days previously multiplied by 10 – 20 before being divided by deaths now - a very different figure.
Just completed 3 weeks of 'proper' isolation, not this 'you can pop out for a stroll' isolation :) It's clearly affecting my brain!
What are the chances of meeting an infected tiger?
> The Chances Of Meeting An Infected Person... depend on the percentage out there, and how many you meet.

That's it, isn't it?

The percentage out there isn't known, thanks to the huge lack of testing, but what seems to be the case is

a) it varies from area to area
b) an average of about 3.3% (1 in 30) seems to be widely accepted
// The percentage out there isn't known,//
yeah but no but
that is my point - isnt the =ve running at 10% ? 8k +ve out of 80k tested with symptoms so you can say it will be less than that ( and more than 0)

so to my mind it is known - you have a band within which
even tho you dont know it to 3 dec places

but you then have to decide what the chance that each encounter results in an infection - given that the fella over 5 d or thereabouts will infect 2.3 other people

oops not sorry he wanted the chance of meeting not the chance of getting infected from any one encounter
( depends of course if were an close enounter or a brief encounter hur hur hur)
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Ellipsis, my question was posted under Science rather than News and I only mentioned Covid19 to give it a topical relevance.
Your 1/33 for infections may well be accurate and I would not like it higher than that, considering that you may see (as opposed to have contact with) that many people as you visit local shops.
Some people here prefer to work with deaths stats because they are certain but my problem with that is that confirmations from different hospitals can be very uneven. So the logarithmic grouping of usually three days would show untidy and inaccurate entries, suggesting that a less helpful seven-day running total would produce a more reliable graph.
On a brighter note, survival rates should improve eventually on some charts, if not doing so already, because some people may have died at a time when specialist facilities were not readily available to treat them, and hopefully that is less common now.
NICKORWAN, the figures for daily deaths are not up to date either. They reflect the number of deaths reported, not those who have died, in the most recent twenty-four hour period.

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