For example, 712 of 3700 people on DM became ill, which gives crude AR = 19.24 per cent.
(I think you meant DP for Diamond Princess)
This is a lower bound on the number infected. From what I understand, PCR viral detection peaks in the 80% to 90% range a few days after exposure, but then falls off to 20% or lower after about a week or two on average (but at some variable rate depending on immune interaction as you mention).
They didn't test everyone quick or frequently enough such that the known case number is a tight bound on the true case number. From what we know on PCR false negative time curve, it seems likely that the true AR on DP is anywhere from 30% to as high as 60%.
If we model the PCR detection time curve as being age dependent (which seems reasonable), then that predicts that the AR was probably above 50% on the submarine and perhaps DP, it just wasn't all detected. For the submarine in particular the population is probably skewed a bit younger/healthy and thus more mild/asymptomatic cases that fight it off quickly.
Most places in europe seem to be in or near mid sigmoid at this point (with the US probably not far behind), but it's too early to tell whether that's due to high AR and herd immunity or lower AR and social distancing.
The Kinsa data seems to suggest that the AR was on average only about on order flu AR, but perhaps higher in some hotspot cities (where the implied AR is perhaps larger than flu). That data also suggests social distancing & closures were effective, but there are some counterexamples (like miami ) where it seemed to peak naturally too early to explain by (late) social distancing.
There's also the Japan mystery, which should have a high AR at this point. Right now the most likely explanations I can think of are either flu like severity/mortality that's not that noticeable when you aren't directly looking for it, or a strain difference.
Strain differences are *extremely* unlikely. No strain right now is more than about 40 nucleotides different from any other, all kinds of deep branches have gone all over the world, most countries have multiple branches from all over the tree, and there just hasn't been enough time in an explovely expanding outbreak for much in the way of evolution to have occurred at all. Most of the observed mutations are silent anyway.
The first serological data on a set of close contacts of hospitalized cases found 16 PCR-positive cases and an additional 7 that developed antibodies but were not successfully caught with PCR tests. Some of which did develop symptoms.
Yes, DP. Lower sensitive of PCR means a lot more of very mild or asymptomatic cases on DM, which have no other manifestations (or people on DP concealed their illnesses).
Let’s here define the “attack rate” (AR) as a share of people in a group which was infected after an infection agent was introduced into the group. For example, it is estimated that swine flu infected 10-15 per cent of the world population in 2009-2010.
Obviously, there is a large difference between AR = 10 per cent and 80 per cent, no matter what is the infection-fatality rate (IFR), as in the first case 8 times fewer people will die.
Crude AR depends on several variables
1) Number of people which never contacted the virus at all (didn’t inhale any virus particles)
1a) Because they were well isolated.
1b) Because they were lucky.
2) The number of people who have physical contact with virus particles but never develop illness:
2a) Those who have a natural immunity to the virus, powerful immune system or special genetics.
2b) Those who have cross-immunity from some other similar viruses or vaccines.
2c) Those who already had the virus in previous time and now became a backbone of the herd immunity.
2d) Those who had so short and mild illness that was not detectable by available methods at the time like PCR, or via self-observation (maybe because of getting only very small viral load).
Attempts to estimate crude AR
It is difficult to estimate the true AR, as it also depends on circumstances, like the age of people in the group, duration of exposure, viral load.
In some cases, we could measure the crude AR, but can’t guess which of the six listed above causes explain it. For example, 712 of 3700 people on DM became ill, which gives crude AR = 19.24 per cent.
Another case: “In total, 15 members of the 58-strong crew reported sick with slight flu symptoms, including coughing and a slightly raised temperature. Tests showed eight members of the crew had or had recovered from coronavirus, the defence ministry said.” which implies crude AR = 25.8 per cent. People inside the submarine have almost no chances to escape the virus, as they are locked inside the same space for days, so it is probably an upper level of crude AR for this age group.
In another case, 9 of 48 passengers of the bus (assuming it was full) became infected, including some who were in a remote part of the bus or board after the patients departed. which implies crude AR = 19 per cent.
These groups include only a small number of children below 18, and we didn’t hear anything about the explosion of the virus in schools, so we could adjust our estimation of crude AR for the whole population. 13 per cent of the population in Italy is below 14 years old , thus it is around 18 per cent below 18, and thus we should dilute AR by the factor of 0.82. 25.6x0.82 = 20.9.
So, different estimates give us the crude AR around 20 per cent (but it is for relatively short-term exposure, not for years-long periods).
Possible causes of low crude AR and coping strategy
The main question (the answer on which has tremendous importance for our coping strategy): what is the main reason for this relatively low crude AR? There are three lines of thoughts about it and three corresponding strategies:
To solve this, we need serological population studies on CV antibodies. Another argument for (2) will be a possible peak in European infection rates in next days if some countries will reach the level implied by the crude AR. For example, there was a research that up to 15 per cent of the population of Spain is already infected (as of 28 of March 2020). In that case, we should observe the peak of hospitalizations in Spain in the next 1-2 weeks.
ADDED: In Skagit choir 75% fell ill. The average rate of infected was 67, according to the article, so obviously the attack rate is age-dependent - and also viral-load dependent. "The youngest of those sickened was 31, but they averaged 67, according to the health department."