After reading comments on a Guardian report it is obvious that most people just can't grasp the concept.
The idea that say with R=3 means that each person passes it on to 3 others is easy, but the relation to increasing or decreasing rates of infection seems to be eluding people.
Re: How difficult a concept is the R value?
Posted: Fri May 01, 2020 11:38 am
by lpm
I think it's being explained quite well? They've dropped the naught in R0, keeping to simple language.
It's always a struggle to comprehend the depths of stupidity, though.
I think it's being explained quite well? They've dropped the naught in R0, keeping to simple language.
It's always a struggle to comprehend the depths of stupidity, though.
R_0 is the rate for the virus with no special measures being taken, and no experience based immunity in the population. It becomes R once the population environment seen by the virus changes, whether through quarantine measures or increasing immunity in the population.
But most people don't have the ability to visualize or intuit the effects of changes in exponents of exponential/geometric processes. This is usually down to lack of experience of thinking numerically about those kinds of processes, rather than whatever it is that IQ measures.
After reading comments on a Guardian report it is obvious that most people just can't grasp the concept.
The idea that say with R=3 means that each person passes it on to 3 others is easy, ...
Easy, but wrong. The important bit omitted is that it is an average. Unfortunately the wording is a very common way to express averages even though it is quite deceptive. For example, patient 31 in South Korea is thought to have infected 70 people. To keep the average at about 3 that means that many of those must have infected fewer than 3 - quite likely many infected nobody. When R=3, it's quite easy for someone to infect more than six others, but clearly impossible to infect fewer than zero. This means that there is a bias whereby some people are far more important than others. If they could be identified and targeted, then it would be much easier to get the number of new cases down. Unfortunately, not much seems to be known about what's different about them, so we're left with general principles and guesswork, meaning we have to throw everything we can think of against it and hope we've covered everything important.
The idea that say with R=3 means that each person passes it on to 3 others is easy
But the idea that say with R=0.75 means that each person passes it on to 0.75 others is not.
Also, exponential growth is hard to understand. Really hard. Humans don't think linearly but logarithmically. If I say that the UK budget for health is £145,000,000,000, the budget for the Home Office is £10,700,000,000, and the budget for transport is £2,100,000,000, you tend to think that the difference between health and HO is about the same as the difference between HO and transport: ten times. You don't think of it like a metre rule, where 92 cm of its length represents health, and hand's-width represents HO and a few mm on the end represents transport.
The idea that say with R=3 means that each person passes it on to 3 others is easy
But the idea that say with R=0.75 means that each person passes it on to 0.75 others is not.
Also, exponential growth is hard to understand. Really hard. Humans don't think linearly but logarithmically. If I say that the UK budget for health is £145,000,000,000, the budget for the Home Office is £10,700,000,000, and the budget for transport is £2,100,000,000, you tend to think that the difference between health and HO is about the same as the difference between HO and transport: ten times. You don't think of it like a metre rule, where 92 cm of its length represents health, and hand's-width represents HO and a few mm on the end represents transport.
I don't understand what you mean by thinking 'linearly not logarithmically'. If I was thinking of your example in terms of metre rules: health would be about up to my shoulder (1m45cm), HO would be about a hand's width(10cm) and transport would be a little thicker than my thumb (2cm). Not mm, cm.
Unless you've accidently added more zeros to tranport than you meant to?
The idea that say with R=3 means that each person passes it on to 3 others is easy
But the idea that say with R=0.75 means that each person passes it on to 0.75 others is not.
Also, exponential growth is hard to understand. Really hard. Humans don't think linearly but logarithmically.
With a logarithmic y-axis an exponential is a straight line.
So why does thinking logarithmically make understanding exponential growth harder?
Re: How difficult a concept is the R value?
Posted: Mon May 04, 2020 8:57 pm
by Sciolus
Clearly I ought to try to explain my brane-vomit better, but I'm not sure I can. I shall just refer you to the fable of the rice and the chessboard, or you could ask a passing stranger how long it would take a single person to infect the entire UK with a doubling rate of 3 days Spoiler:
Clearly I ought to try to explain my brane-vomit better, but I'm not sure I can. I shall just refer you to the fable of the rice and the chessboard, or you could ask a passing stranger how long it would take a single person to infect the entire UK with a doubling rate of 3 days Spoiler:
about 26 doublings so 2.5 months
.
Did you mean that people do think linearly, rather than logarithmically? Otherwise I'm still struggling.
After reading comments on a Guardian report it is obvious that most people just can't grasp the concept.
The idea that say with R=3 means that each person passes it on to 3 others is easy, ...
Easy, but wrong. The important bit omitted is that it is an average.
I assumed that "on average" was given. Obviously not.
Only if you're explaining to reasonable people.
Re: How difficult a concept is the R value?
Posted: Thu May 14, 2020 9:43 pm
by sTeamTraen
Can anyone with subject matter knowledge explain to me how the current R value in a country is typically calculated?
We hear reports like "It dropped to 0.7 in Germany, then they unlocked and it went to 1.1, now it's below 1 again", so presumably there is some formula, but I don't know it it's published anywhere. For example, I guess that it might be some function of logarithm of the delta in new cases since last week, since growth is itself exponential (whether positively or negatively), but I've never seen the precise mechanism discussed anywhere.
Re: How difficult a concept is the R value?
Posted: Thu May 14, 2020 10:15 pm
by shpalman
You can see directly from the data if the number of cases is increasing (positive exponent, R>1) or decaying (negative exponent, R<1) exponentially. The exact value of R would depend on at least an assumption about the time an infected person is infectious for, so that you can convert from infections per day into infections per infected person.
You can see directly from the data if the number of cases is increasing (positive exponent, R>1) or decaying (negative exponent, R<1) exponentially. The exact value of R would depend on at least an assumption about the time an infected person is infectious for, so that you can convert from infections per day into infections per infected person.
Yes, you can see whether R is greater or less than 1 (or at least the situation a few days ago, when the tests were carried out) but I think you need population sample testing to actually work the R value. If you change the number of tests you perform, or the testing criteria, I don't think you can even say whether increases or decreases are due to changes in systematic sampling error or due to changes in infection.
You can see directly from the data if the number of cases is increasing (positive exponent, R>1) or decaying (negative exponent, R<1) exponentially. The exact value of R would depend on at least an assumption about the time an infected person is infectious for, so that you can convert from infections per day into infections per infected person.
Yes, you can see whether R is greater or less than 1 (or at least the situation a few days ago, when the tests were carried out) but I think you need population sample testing to actually work the R value. If you change the number of tests you perform, or the testing criteria, I don't think you can even say whether increases or decreases are due to changes in systematic sampling error or due to changes in infection.
Well yes, first you need an estimate of the actual number of new infections. If you're not just going to use the number of positive tests then you need some model to correct for the incomplete and biased sampling. There are all sorts of ways to do that.
Then, once you've done that to get an estimate of the actual number of cases, you can see if the number of cases is increasing (positive exponent, R>1) or decaying (negative exponent, R<1) exponentially. The exact value of R would depend on at least an assumption about the time an infected person is infectious for, so that you can convert from infections per day into infections per infected person.
You can see directly from the data if the number of cases is increasing (positive exponent, R>1) or decaying (negative exponent, R<1) exponentially. The exact value of R would depend on at least an assumption about the time an infected person is infectious for, so that you can convert from infections per day into infections per infected person.
Yes, you can see whether R is greater or less than 1 (or at least the situation a few days ago, when the tests were carried out) but I think you need population sample testing to actually work the R value. If you change the number of tests you perform, or the testing criteria, I don't think you can even say whether increases or decreases are due to changes in systematic sampling error or due to changes in infection.
Well yes, first you need an estimate of the actual number of new infections. If you're not just going to use the number of positive tests then you need some model to correct for the incomplete and biased sampling. There are all sorts of ways to do that.
Then, once you've done that to get an estimate of the actual number of cases, you can see if the number of cases is increasing (positive exponent, R>1) or decaying (negative exponent, R<1) exponentially. The exact value of R would depend on at least an assumption about the time an infected person is infectious for, so that you can convert from infections per day into infections per infected person.
The thing is that even if you have a stable test, of say those showing symptoms, a constant R0 and a large number of asymptomatic infections could give a similar result to an increasing R0 but a small number of asymptomatic infections.
Re: How difficult a concept is the R value?
Posted: Sat May 16, 2020 1:20 pm
by shpalman
If the symptomatic infections are a constant proportion of the total then all it does is shift the straight line on the semilog plot of known infections up or down but doesn't change its slope. i.e. the exponential rate is the same.
Let's say only 20% of the true infections show up with symptoms which get counted in the stats. This makes an unexposed person 5 times more likely to catch the virus. But only 20% of those exposures will develop symptomatic infections which get counted.
It won't matter until the total number of infections becomes a substantial fraction of the population so that asymptomatic carriers are more likely to meet other asymptomatic carriers (or people who have already recovered) rather than unexposed individuals. There are people arguing that this is happening and the peak in infection rates is due to this effect. It would be nice because it would mean herd immunity, but I really don't think it's the case unless you're in the hottest of hot spots.
The above consideration is skewed by the detection and quarantining of symptomatic cases, but we know there are a couple of infectious but asymptomatic days before symptoms develop, as well as there being completely asymptomatic cases which never get detected.
If the symptomatic infections are a constant proportion of the total then all it does is shift the straight line on the semilog plot of known infections up or down but doesn't change its slope. i.e. the exponential rate is the same.
Let's say only 20% of the true infections show up with symptoms which get counted in the stats. This makes an unexposed person 5 times more likely to catch the virus. But only 20% of those exposures will develop symptomatic infections which get counted.
It won't matter until the total number of infections becomes a substantial fraction of the population so that asymptomatic carriers are more likely to meet other asymptomatic carriers (or people who have already recovered) rather than unexposed individuals. There are people arguing that this is happening and the peak in infection rates is due to this effect. It would be nice because it would mean herd immunity, but I really don't think it's the case unless you're in the hottest of hot spots.
The above consideration is skewed by the detection and quarantining of symptomatic cases, but we know there are a couple of infectious but asymptomatic days before symptoms develop, as well as there being completely asymptomatic cases which never get detected.
Yes, I was ignoring the first generation infections from asymptomatic people. Which made my maths pretty wrong.
As to your second point, the mortality rate seems to be of the order of 1-5% for those populations which have been sample tested or tested well. So, as you say, it seems still in the region where we can pretty much ignore the non-susceptible proportion of the population. Especially given the other uncertainties in the data.
This is interesting: for most people R is effectively zero, and the contagion is dominated by a relatively small number of super spreaders.
I've been reading a lot on graph theory and its applications recently (for unrelated reasons). This seems to be a common feature of epidemics, and quite a common feature of real-world networks in general. The degree distribution (number of links per node) tends to be a power law, so most nodes have few links and a few have loads. (In general you wouldn't model nodes with zero links in your network, I suppose)