Yes I think that
You barely need 100 test kits and 100 random persons to check that “50% hypothesis”
is a good one.
But maybe the antibody test kits were not around until very recently? There is talk of distributing them for free via Amazon etc. Unsurprisingly I’ve just seen an email from some wide boy flogging them for £30 
it would become cheaper and cheaper as time goes by
To argue that is to argue that the number of Aston Martins in the car parks of private hospitals should decrease, which is a mathematical impossibility.
Now look at which countries have the highest proportion of privately (insurance) funded hospitals. In Europe, Germany is perhaps #1. No wonder they have lots of capacity.
Jacko wrote:
The impression I have is that they said they would (a) protect the old/vulnerable as far as possible while (b) allowing others to catch and pass on the disease in a more or less controlled manner so as to avoid swamping the healthcare service. I also got the impression, at every stage, that control measures would be adjusted as and when required.
Agree, it was those at risk to stay home (+70yo and flu-like), the rest just carry as normal, seems to me like a gamble with 70% of population with no clues on risk to the non-at-risk 70% population, also you can’t backtrack on this when it fires or control anything if they got it wrong kwlf wrote:
It may get back again into fashion after 1 month lockdown once treatments, protection and testing capacity is around
It’s not an insane strategy. it might actually work but surely not like all-in gamble on first round of poker…
Ibra, I think the epidemiologists take it to a high art
You can simplify a lot, take previous statements on daily rate of cumulative infected cases (25%-30% increase per day, I think this come up in many graphs/discussions), the first case in UK was detected end Jan, if you believe that is wrong and the first case in UK is Dec/Jan (Ski or Xmas, NYE holiday most likely, few people travel outside those, let alone infected) and also I think 4 weeks is about decent time lag for things to get flagged in the healthcare system 
Then you have a reliable estimate of number of infections, this does not require exact knowledge of the true number of infected, just the daily trend on those tested and the real date of patient 0, latter on things get non-linear and even up/down with awareness but up to today it is really as simple as an exponential/geometric series, of course you can do sophisticated maths or test full population later on
kwlf wrote:
FWIW an illness with an R0 of 2 will take an infinite amount of time to infect 50% of the population. An illness with an R0 of 4 will take an infinite amount of time to infect 75% of the population but a finite time to infect 50% of the population
I don’t think that is correct. For R0 = 2, 50% of the population is the middle of the S curve, where the growth is almost linear and starts to flatten, and the number if people who are currently ill will start to decrease one incubation period after that point.
I believe that is because the replication rate R at any time is (R0 * susceptible), so at the beginning R = R0 if 100 of the population is susceptible, and when half the population is has been infected (and hence is no longer susceptible because they are already ill, recovered or dead), R = R0 / 2 = 1.
It then takes “forever” to reach 100%.
I don’t think that is correct. For R0 = 2, 50% of the population is the middle of the S curve, where the growth is almost linear and starts to flatten, and the number if people who are currently ill will start to decrease one incubation period after that point.
Look up herd immunity thresholds. R0 is the average number of people who will be infected by a carrier in a naive population. If the population is 50% infected, the carrier is half as likely to meet a susceptible, uninfected individual as before, so if R0 is 2, the average number of people he will infect is 1, not 2. Anything below that and the disease will die out. So the proportion of the population who get infected will asymptote to 50%.
p.s. if the disease is rare, then you only need to test 6 people to show that less than 50% of the population is infected. If they all test negative the 95% confidence interval for the prevalence of the disease will be 0-46% i.e. less than 50%.
Here is a thought regarding the probability that eventually you will get the Wuhan Virus. If it is as infectious as they say it is, the rate will increase.
Its all math. Fortunately the fatality rate on the Cruise ships was .8%. Most of the passengers were >60 yrs old. 2000 passengers 1000 crew.
The other good news is that there are currently used medications which seem to have very promising outcomes.
I have a feeling this kind of exchanges aren’t going to help keep this thread friendly ….
Perhaps I was a little brusque. I don’t think it’s fair to criticise travel for the pandemic. It’s true that South America was geographically isolated from many infectious diseases until 1492, but since that point the question has been about how fast infections spread from one country to another rather than whether they do.
The pandemic was caused by spread from animals. Restricting travel would do nothing to prevent this from recurring.
Even the 1918 ’flu spread throughout the globe within a year. Once a few cases reached any continent it was virtually inevitable that it would spread within that continent unless you implemented strict measures as we are doing now.
SARS and Ebola were kept at bay partly through very hard work, but also partly because they were not as good at spreading as SARS-Cov2 seems to be.
Airline travel spreads pandemics faster leaving us less time to prepare for them, but restricting it wouldn’t prevent them. I agree though that the airlines are in for a very hard time. Unless a vaccine is made I think people who are not exposed to the virus may become reluctant to travel by air until the virus has died out worldwide, assuming this happens.
kwlf wrote:
R0 is the average number of people who will be infected by a carrier in a naive population. If the population is 50% infected, the carrier is half as likely to meet a susceptible, uninfected individual as before, so if R0 is 2, the average number of people he will infect is 1, not 2.
Which is correct – R = R0 times the percentage of population that is susceptible, so 1 at 50%
Anything below that and the disease will die out. So the proportion of the population who get infected will asymptote to 50%.
This is wrong, and quite obviously so. Since every infected individual will infect another one, infections are obviously still happening. The asymptote is where R reaches zero, and nobody else is getting infected.kwlf wrote:
Look up herd immunity thresholds
“Herd immunity” is really only meaningful if there are only few infections, and the spread is so slow that you have to take into account birth rates… not after it has ran away.
The estimates that the disease may infect 60-70% of the population are based on herd immunity thresholds. As the rate of infections will decrease as you approach the threshold it’s true that one infected person will infect another, but there will hardly be any of them so R will be infinitesimal and infection levels will not go to 100%
I grant you that the model falls down in certain circumstances e.g. if someone is a chronic ‘super spreader’ like Typhoid Mary.
Yes, R0 or transmission is only relevant at time 0 or at the start of epedemic, it decays with the number of infected and the time one is infectious and increase with number of suceptibles, but it is what drives the “second exponential segment” before peak, which one call “media panic” or “seriousness” and that is when action is needed, not before and not after, here is a model/calculator,
https://gabgoh.github.io/COVID/index.html
Also Rt depends on things that are not modelled for which we have no clue yet such as double exposures, herd immunity and future mutations, for example SARS1 went into the bin in Europe as it simply mutated in the heat of human transmissions, this does not seem the case for SARS2 today but it is too early…
https://www.nature.com/articles/s41598-018-33487-8
My point on using a toy model is to guess the number of those infected simply by guessing the date for “case 0” as there is lot of institutional interia and testing/sampling time lag, I think the number of infected in UK is in 1% to 10% of population not the reported “few 10k” or “Oxford 50%”
You can have a better guess by simply asking how many celebrities have SARS2 virus? and how many famous people are around? Famous is relative but 1 in 5000 is a good number (comes from counting Wikipedia pages of english living population, credit goes to Samuel Arbesman from Harvard), I am sure the number of celebrities who has COVID19 is higher than 5 and sure less than 1000 and there is zero time lag for this information
At the end of the day, all these models are imperfect.
