How many people have been exposed to Covid-19 ?

In the last few days, there have been quite a few reports of studies suggesting that the number of people who have been exposed to Covid-19 is far larger than previously thought. These studies have been based on testing for antibodies against coronavirus (it is unclear whether they are specific to Covid-19, or might reflect exposure to other coronaviruses).

I’m finding it difficult to square these estimates with inferences from direct testing, which (as I understand it) tests whether people currently have the disease. This is a point on which I would really like to see a clear explanation from an epidemiologist, but I haven’t seen one, so I am going to set out my own thoughts.

Alert: Unlike my discussion of the exponential growth rate R, where I was confident in the analysis and rapidly proved correct, this is an amateur effort and I could easily be missing something crucial

Suppose that

  • the virus has been around for some number of days D
  • infected people will give a positive response to a direct test for d days
  • the proportion of positive test results in a random sample of the population is p

Then, as a first approximation, the proportion of people ever exposed is (D/d)p. To estimate D, I’ll assume that very few* people outside China were infected before 1 February, which gives D = 84 as of April 25. I’m less clear about d, but 14 days appears to be the standard estimate for asymptomatic cases. That gives D/d = 6.

The big problem is p. Most places are only testing people who are at high risk because of symptoms or known contacts. Iceland gave 1800 tests to randomly selected volunteers in March, and got a positive rate of 1 per cent, suggesting that the proportion ever exposed would be 6 per cent. That’s a lot of people, but nowhere near enough to make herd immunity a relevant possibility.

Any ideas?

  • Some were, it’s clear, but if the numbers had been large, we would have seen many more deaths.

44 thoughts on “How many people have been exposed to Covid-19 ?

  1. If you are interested in the case fatality rate, my impression is most of the current testing regimes give you a reasonable idea in comparison with other corona viruses (but not other classes of pathogens). They test people with overt symptoms, and endemic coronaviruses typically have lots of very mild or zero symptom cases (SARS was an exception, and easily dealt with for that reason).

    The other use for random sampling is some estimate of the potential reach of the disease and of herd immunity. All the estimates I have seen are that, even in hot spots, less than 10% of the population has been infected, while herd immunity needs rates higher than 60% – much higher if immunity does not last long.

    Re previous post – this may well settle into a pattern where it’s endemic with periodic outbreaks. In which case the economic recovery will not be quick.

  2. John,

    Point 1 – Immunity

    Don’t assume immunity is possible or if possible is complete, for the individual or for the herd. The relevant empirical facts are not clear yet about this pathogen, SARS CoV2 which causes COVID-19 disease. The most likely scenario, given the family of viruses this virus belongs to, is partial immunity decaying over time and even largely decayed within 18 to 24 months (or less!)

    “The truth is, our immune responses to this virus aren’t likely to be permanent or perfect.” – Christie Aschwaden – Wired.

    https://www.wired.com/story/sorry-immunity-to-covid-19-wont-be-like-a-superpower/

    Herd immunity could well be a mirage and COVID-19 could re-appear yearly or twice yearly etc in pandemic waves. It could also mutate into variants far worse and/or far less worse or anything in between. These are are all unknowns at the present time.

    The better course of action is to go for complete eradication which you have also said. At first, it would have to be “eradication in one country” and you have spoken about the quarantine controls necessary for this.

    Point 2 – Infection Rate

    It has been my lay person guesstimate that infections could be 2 to 10 times higher than confirmed cases. That’s a wide margin of error of course.

    Don’t we need a point in time test of a valid random sample of the whole population (of all age groups, sexes etc. too) to get the overall infection rate at that point in time? However, that sample would be skewed by those who actively sought a test on that given day due to symptoms. How are they to be treated? If entirely added in to the sample or entirely excludedfrom the sample would not both of these stratagems skew the results (in opposite ways)? You probably know of some statistical methods which could adjust for these biases.

    Point 3 – Sequelae

    Assuming an ostensibly harmless infection is harmless and will be harmless indefinitely ignores the issue of medical sequelae. We do not yet know the sequelae of COVID-19 in adults or children. It is too early for this data to be observed, analyzed and made available.

    Summing Up

    We should proceed with great caution and work for eradication. Economic damage is secondary and manageable if we use fiscal policy and general democratic socialist economic principles.

    There are beneficial ecological and sustainability effects from this partial shutdown. These may be listed on the benefit side of the benefit-cost equations. I for one think it’s great that pollution is down, climate change will be forced less quickly and turtle hatchings (for example) are up.

    “Baby leatherback sea turtles thriving due to COVID-19 beach restrictions” – Live Science Online).

  3. WRT immunity, given the increased exposure by HCWs to COVID you would think that they would have built up immunity. And if COVID has been in the community for longer than thought, as some have hypothesised, HCWs should be virtually immune to COVID.

    But they haven’t and in Italy the stats indicate ~11% infection in HCWs.

    This pool of immunity could be mythical.

  4. Don’t imagine a vaccine is possible, let alone certain.

    AFAIK we don’t yet have a vaccine for *any* coronavirus, let alone one that can be manufactured in sufficient quantity to keep worldwide herd immunity up. It’s possible that the vaccine we get will make the infection less severe and the vaccine effect wears off after months rather than decades.

    Ebola is one recent success, but that really didn’t have the funding or focus that covid-19 does so that alone should mean that if a vaccine is possible it will be found in less than five years. Rich people’s lives matter more.

    Earlier immune studies also suggest that having survived a coronavirus once doesn’t mean you will survive it next time, especially for people with long-term ill effects (especially lung damage).

  5. One bad case would be that we eventually learn to live with circulating waves of covid-19 that subside once there’s local herd immunity/sufficient lockdown, and only stop when the virus mutates and loses potency. The timeframe for that… well, you could look at the various herpes viruses and wonder when exactly chicken pox will just go away of its own accord.

    Which all suggests that planning for a return to normal in a month or even a year is optimistic (or fatalistic, if you think we’ll just give up and decide to take our chances). Cycling on the roads of inner Sydney suggest that the lockdown is already wearing thin for many people.

  6. https://publicaddress.net/hardnews/has-iran-found-an-effective-covid-19-treatment/

    Letter from James Freeman, 21/4/20

    For those of you who like executive summaries, here it is. It may surprise you to know that doctors in Iran have commenced 109 clinical trials on treatments for COVID-19 and have recently announced that they have found a cure, where that cure looks like no ICU deaths and rapid recovery for patients.

    While Iran has not announced the name of the drug it can be accurately deduced via an analysis of their clinical trials database.

  7. How are herd immunity calculations affected if 80% of infected people are asymptomatic and unable to pass on the infection? Is this not effectively similar to having already an intrinsic herd immunity of 80%? Does this explain the low positive return rate of the random testing done in Iceland and the suggested low proportion of those ever exposed?

    What do the 20% who develop symptoms have physiologically in common outside of known vulnerabilities, ie the otherwise healthy without co-morbidities? Should research on prevention and cure be mainly targetted there as for other aspects of health care? Is the 80-20 rule somehow applicable?

    https://theconversation.com/why-do-some-people-with-coronavirus-get-symptoms-while-others-dont-135546

    https://en.wikipedia.org/wiki/Pareto_principle#Other_applications

  8. “”Way more people may have gotten coronavirus than we thought, small antibody study suggests

    Editor’s note: This story was updated at 12:00 a.m. E.D.T. on Sunday, April 19

    Way more people may have gotten coronavirus than we are detecting.

    That’s the takeaway from a small study of coronavirus antibodies in more than 3,000 people in Santa Clara County, California. The results suggested that between 2.5% and 4.2% of people in the county have contracted COVID-19, which is 50 to 85 times greater than the number of cases being reported at the time. Not everyone is convinced the true prevalence is that high, however, with some saying the antibody test the researchers used was not reliable.

    However, this type of antibody testing, or serologic study, should be rolled out more broadly, epidemiologists told Live Science.
    https://www.livescience.com/coronavirus-antibodies-widespread-in-santa-clara.html

    Published in;
    COVID-19 Antibody Seroprevalence in Santa Clara County, California
    https://www.medrxiv.org/content/10.1101/2020.04.14.20062463v1

    https://paloaltoonline.com/news/2020/04/17/stanford-study-more-than-48000-santa-clara-county-residents-have-likely-been-infected-by-coronavirus

    But!
    “”Concerns with that Stanford study of coronavirus prevalence

    Reading through the preprint
    “Anyway, after receiving the above email, I clicked though and read the preprint, “COVID-19 Antibody Seroprevalence in Santa Clara County, California,” by Eran Bendavid et al., which reports:

    “On 4/3-4/4, 2020, we tested county residents for antibodies to SARS-CoV-2 using a lateral flow immunoassay. Participants were recruited using Facebook ads targeting a representative sample of the county by demographic and geographic characteristics. We report the prevalence of antibodies to SARS- CoV-2 in a sample of 3,330 people, adjusting for zip code, sex, and race/ethnicity. . . . The unadjusted prevalence of antibodies to SARS-CoV-2 in Santa Clara County was 1.5% . . . and the population-weighted prevalence was 2.8%.

    “That’s positive test results. Then you have to adjust for testing errors:

    “Under the three scenarios for test performance characteristics, the population prevalence of COVID-19 in Santa Clara ranged from 2.5% to 4.2%. [I’ve rounded all numbers to a single decimal place for my own sanity. — AG]

    “To discuss this paper, I’ll work backward, starting from the conclusion and going through the methods and assumptions.

    “Let’s take their final estimate, 2.5% to 4.2%, and call it 3%. Is a 3% rate of coronavirus antibodies in Santa Clara county a high or a low number? And does this represent good news or bad news?

    “First off, 3% does not sound implausible. If they said 30%, I’d be skeptical, given how everyone’s been hiding out for awhile, but 3%, sure, maybe so. Bendavid et al. argue that if the number is 3%, that’s good news, because Santa Clara county has 2 million people and only an estimated 100 deaths . . . 0.03*(2 million)/100 = 600, so that implies that 1/600 of exposed people there died. So that’s good news, relatively speaking: we’d still like to avoid 300 million Americans getting the virus and 500,000 dying, but that’s still better than the doomsday scenario.”
    https://statmodeling.stat.columbia.edu/2020/04/19/fatal-flaws-in-stanford-study-of-coronavirus-prevalence/

    Although one phone call in Australia may solve for ‘p’;
    https://www.doherty.edu.au/our-work/institute-themes/viral-infectious-diseases/emerging-infections/2019-novel-coronavirus/about-2019-novel-coronavirus

    Then use Vo as test data?
    “Professor Cristani directs the Molecular Medicine Department in Padua. His team carried out 3300 coronavirus swabs on the entire population of one of the initial 11 lockdown towns in northern Italy, Vo Euganeo, the only one in the Veneto region.

    “No one else decided to test every single member of the lockdown community. The results immediately showed that 3 percent of all those tested were positive. “We did not realize at the time this was a huge number but we immediately were able to see that the majority of those who were positive did not have any symptoms”, said Cristani.

    “The population was tested again after the two-week lockdown and “the lesson we learned is that isolating all positive cases, whether they were sick or not, we were able to reduce transmission by 90 percent and we found that all those who were still positive were all without symptoms”.
    http://www.rfi.fr/en/europe/20200316-the-hard-lessons-of-italy-s-devastating-coronavirus-outbreak

  9. is there a lag between infection and testing positive for infection?

    ie day 0 get infected test -ve
    day 1 test -ve

    day n test +ve

    and when does person become a spreader?

  10. If there are more people out there producing significant quantities of the virus than expected, we should be able to determine this with enough random reverse-transcriptase polymerase chain reaction tests.

    Of course, it may not make sense to do that if using limited sources in a more focused way may is likely to save more lives.

    So we could instead attempt to determine if there are disease clusters coming out of apparently no where started by this invisible army of asymptomatics. And if they don’t transmit, they are not so important from an immediate public health perspective.

  11. Much speculation and little reliable data as yet. I am keeping my mind open on real infection numbers, immunity issues, vaccine issues and treatment issues.

    Meanwhile, in Australia where it appears eminently feasible, we should go for eradication, by lock-down if necessary. This would include not opening schools for this term.

  12. There is no reason to doubt that antibodies are effective against the virus. How else do most infected people recover? The legitimate questions are over the degree of protection antibodies offer if the virus mutates (absent an effective treatment, it has no Darwinian reason to do so), and decay of the immune trsponse over time (nil for smallpox).

    Even rear-envelope models should consider the 30% false negative rate in single tests. This won’t be falling, as public health agencies reasonably give priority to cheap and fast mass tests over accuracy. A 70% accurate test, applied on a large scale in a 3T scheme, could by itself reduce R below 1.

  13. if the numbers [infected] had been large, we would have seen many more deaths

    Not if the true mortality rate was far lower than the current rate which is based on KNOWN cases.The infections left untested are in precisely those at minimal risk of dying.

    To illustrate, a very recent survey suggests 2.7M people in New York have already been infected ( https://www.reuters.com/article/us-health-coronavirus-usa-new-york-idUSKCN2252WN ), which would make their mortality rate a full order of magnitude (0.5% vs 5%) lower than their press has been quoting.

    If Covid is in fact much less deadly than we believe on the basis of what happens with KNOWN cases then the case for an early end to lockdowns to revive the economy becomes much stronger.

  14. Slightly OT, but interesting. Two polities in the island of Ireland offer a real-time experiment with two different approaches to controlling the virus epidemic,with the same index case. The result is a clear win for the Republic’s policy of widespread testing and contact tracing, against the Northern Irish = British policy focusing on hospital capacity. The author is an emeritus professor of social policy at Queens’ U . Belfast.
    https://www.irishtimes.com/opinion/coronavirus-ireland-is-one-island-with-two-very-different-death-rates-1.4234353?fbclid=IwAR0m5lyYp1De9560HG-vYap4cIoGzlSHBH22XsLQJteq4WPOzPxfL8QrH44

  15. “, which would make their mortality rate a full order of magnitude (0.5% vs 5%) lower than their press has been quoting.”

    That must have been some tabloid press if they suggested that 5% was the actual mortality rate. Maybe the reporting was just that´s the mortality rate accourding to the offical statisc (footnote which is uterly unreliable at the moment). 10 Times more infected than confirmed cases isn´t really one of those “out there” numbers (and its a world away from herd immunity aswell), the out there numbers are more the 20 times ones. 5-10 more infected than confirmed cases seems to be the standard range suggested in regions with a decent test capacity, which New York sure isnt even. Its on the contrary one of those complete breakdown and chaos regions where all numbers are uterly wrong Ther are certainly also many unreported corona deat there.. Such has already been confirmed by mortality statistics for the worst regions in Italy with estimated actual death up to arround 3-4 times higher than the reported numbers and about 2 times higher for the entire UK (which albeit also has a particular questionable reporting systems).

  16. Dont know which reports the op is refering to exactly- the two Swedish ones appear to have been redacted already for basic errors. One of them simply appears to have had a calculus error – which caused such hilarious results that they were already spotted by journalists during the presentation, so one has to wunder how that one could have possibly been published that way. Another one seems to have misshandled the probes in the lab.

  17. Hi John. Proportion of people ever exposed depends on the area under the number of people infected over time curve. Your (D/d)p is an extreme and assumes that p (say 1%) of the population was infected on day 1 (say 1 Feb, D = 84) and a different p every subsequent d (say 14 days). At the other extreme, 0% of the population may have been infected, except for the last days when testing was carried out (Iceland), when the infection rate jumped to p.

    Surely a better first approximation is the average of these, which gives 3.5 % ever exposed [((D/d)p + p) / 2]

    This suggests that the herd immunity solution is an even more deadly path. Regards.

  18. The shut-down has been shown to have significant ecological benefits. Skies have cleared of pollution around the world. We have seen stories such as;

    “Himalayas seen for first time in decades from 125 miles away after pollution drop” – Independent.

    Former Indian cricketer, Harbhajan Singh, tweeted a view of the Dhauladar range from his rooftop in Jalandhar. “Never could imagine that’s possible.. clear indication of the impact pollution has done by us to Mother Earth..” he tweeted. “India’s Central Pollution Control Board said in a report that the lockdown had resulted in a significant improvement in air quality. The India Today Data Intelligence Unit found the air quality index improved by an average of 33 per cent in the country between 16-27 March, SBS Hindi reported.”

    “Coronavirus: Air pollution and CO2 fall rapidly as virus spreads” – BBC.

    https://www.bbc.com/news/science-environment-51944780

    It’s time to think radically. These events show that a large drop in CO2 emissions is possible if we remove non-essential activities from our economy. To prevent dangerous global warming we WILL have to remove most non-essential activities from our economy by simply NOT restarting them after this pandemic if they are high CO2 emitters. This is if there is an “after” because this pandemic may roll on for years. Non-essential economic activities which are high CO2 emitters and/or bring little to no real social benefit should NEVER be restarted. It’s as simple as that if we do not want to unleash catastrophic runaway global warming.

    This would be a frightening, even inconceivable, social and economic prospect to many but it could be done by taking this opportunity to re-orient our entire economy to sustainable activities and renewable energy. High CO2 emission activities which entail non-essential consumption should not be restarted, in the main. The tourist industry is a case in point. Don’t subsidize it and don’t restart it. International tourism is finished for at least two years in any case and perhaps for up to five years, simply by reason of the quarantine measures which will remain necessary for that time. Domestic tourism and use of automobiles should be curtailed by a strong carbon tax added to the price of petrol and diesel for road users. A UBI and JG plus a renewable energy build-out and greater social spending would ease the transition.

    For those who cannot contemplate this change and say it is impossible, it is only their mindset which makes it impossible. If they cannot contemplate sacrifice and frugality to save the planet and the biosphere as a habitable place for humans then they are selecting extinction for the human race.

  19. Hi, if I understand your model correctly, p (estimated to be 1%) refers to the rate of infection among the uninfected. If this is 1%, then the percentage of the entire population having been infected (now assumed to be immune) rises by 1% every 14 days (the period during which an infected person gives a positive response to a test), and so it takes 3 years for around 78% of the population to be infected (365/14 = 26%).

    I assume the Iceland estimate that p = 1% is based on having containment measures in place. (If containment measures were lifted, p would rise, and so achieve “herd immunity” earlier.) Could p be much higher than 1% even with containment measures in place?

    One reason p might be higher is that there is a high rate of asymptomatic infections which the Iceland test does not detect. According to this Science Medical Centre article (https://www.sciencemediacentre.org/expert-comments-on-different-types-of-test-for-covid-19/), it is ideal to combine a PCR test with an antibody test: “When tested alone, the PCR test has a 66.7% detection rate within the first week, whilst the antibody test has a lower 38.3% detection rate.” So if the Iceland random test relied only on the PCR test, it might not have picked up infections among the asymptomatic.

    Hope this is useful!

  20. Iko – “It’s time to think radically. These events show that a large” motivator such as imminent personal/family and/or national economic and sovereign annihilation can do it. It’s worked forever in wartime. It worked for the great pyramid builders of ancient Egypt in undertaking those massive defensive projects. It seems it works if government, the 1%, and most of a population share similarly in the apprehension (belief) and fear. The day will come, albeit too late. ¯\_(?)_/¯

  21. Svante,

    Yep, except that people do not yet believe that personal, family, economic, sovereign, global and human species annihilation are all imminent. Soon, in historical terms, they will believe this. It would help if they could read the science (no tea leaves necessary) and understand these matters. However, it seems not. Faith in capitalist economics still far outstrips scientific literacy and complex systems understanding. But the year is coming and coming soon when all that must change. We will have to change to survive or we will be entirely swept away by natural forces feeding back from the disrupted biosphere system.

  22. The Diamond Princess gives us a pretty good idea of the mortality rate – around 1%. This was a closed population where just about everyone was tested and they received high quality care. The population was older than average, but didn’t include the very frail people you find in nursing homes. So we shouldn’t expect an overall infection mortality rate to be too different from this. (It will be lower because of a lower age distribution in the overall population, and higher if hospitals are overloaded). So the current death rate times 100 gives you a starting point for the infection rate 3-4 weeks ago.

  23. I’m not entirely clear John why you’re trying to calculate the number of people who have been infected with the virus. If you’re aiming for near-elimination as seems to be the aim in Australia and NZ, then the relevant number is the number of people in the community who are shedding the virus – whether they be symptomatic or asymptomatic.
    The number of people infected with the virus would be relevant if you were trying to calculate how far away from herd immunity a particular region or country is.
    Is that your objective?

    The possibility of herd immunity might be a relevant issue in a State like New York where one antibody study indicated that 20% of the population had been infected, and where 1.4% of the population has been diagnosed with COVID-19 (and this 1.4% is a massive underestimate of actual symptomatic cases).
    But there is no possibility of herd immunity in the next 6 months in countries like Australia or Iceland or New Zealand or South Korea where the spread of the virus has been massively curtailed, because the proportion of the population infected at present has to be well under 2%. Why do I say this with such confidence? First, the number of cases diagnosed per million population in Australia is 260 ie .026% of the population. Second, the Doherty Institute through their modelling, estimates that 93% of symptomatic cases are being detected by our testing. 93% seems rather high, so let’s go with a conservative estimate of 80%. Asymptomatic cases as a proportion of all cases is about 40% according to a number of studies, including the Icelandic random sample. But note that the Icelandic researchers warn that the 40% is asymptomatic at the time of testing. So some of the asymptomatic will go on to develop symptoms due to their COVID-19 infection. Therefore 40% asymptomatic is a conservative estimate. Its probably lower.
    Using the above parameters we get an estimate of 541 symptomatic and asymptomatic cases per million population in Australia or 0.05% of the population. This would not be total percent of the Australian population infected, because the above calculation would not account for all of the asymptomatic cases that result from infection from asymptomatic cases. But it would certainly be correct to within an order of magnitude.
    Therefore there is no chance of the Australian population being within cooee of herd immunity at this point in time. The Australian situation is vastly different to New York.

  24. Herd immunity may not occur, indeed very possibly will not occur. We certainly cannot bank on it. Do we have herd immunity against influenza? No. Do we have herd immunity against the common cold (rhinovirus and coronavirus variants)? No. Herd immunity is not possible if individual immunity wears off too fast and/or if the pathogen mutates frequently. There are other dangers too, like a reservoir of the virus getting into wildlife like our bats. People would do well to remember these things and not allowspeculation run ahead of the (as yet early) empirical data.

  25. Since I have been invoked I think I will weigh in. John, I’m not sure that you can get much from D/d. The total number of people infected over time will be integral(exp(-rt)) where r is whatever modified growth rate arises from the dynamics of the infection (r in this expression should itself be a function of time). I think D will only give you an approximate estimate of the number of cases over the initial very linear period of growth. I guess you’re trying to say that the total length of time the virus has been around divided by the length of time people are at risk should give you the number of people currently identifiable? But this doesn’t work because the number of people infected in any d days is growing rapidly. Might it be better to say you need integral(from t to t+d)(exp(-rt))? I don’t think this works at all.

    Also can we please dispense with this discussion of herd immunity. In an epidemic of a disease with an R0 >1.5 you will never achieve herd immunity. There is an equation (called the final size equation) that tells you what proportion of the population will be infected by a disease in terms of its R0, and if R0>2 the proportion is 100%. In the case of influenza probably the final size is about 40% but that is not because of “herd immunity” it is because the virus burnt itself out.

    Herd immunity works for diseases with R0>2 if the herd is immune when the virus is introduced. That is the only way herd immunity works. The required level of herd immunity is then 1-1/R0. So in this case we need 80% of the population to be immune when the first case is introduced in order to stop it spreading. It is not the case that once 80% of the population is infected the disease will stop spreading – with an R0>2 it will continue to infect the whole population once it passes this (completely made-up by Dom Cummings) threshold. Yes you can achieve that threshold at any other point in the epidemic by vaccinating 80% of the remaining susceptible population, but you won’t get it by letting the disease infect those people and have them recover.

    And furthermore, to achieve the level of this (bullshit, made-up) herd immunity threshold “naturally”, you need to infect so many people that it is impossible to avoid infecting people over 60, who will die at rates >1% (to the best of our knowledge, about 20% among confirmed cases aged >80).

    Any discussion of herd immunity through the infection process is dangerous, wishful thinking that will kill your parents and grandparents. Don’t do it.

    As Peter T has pointed out above with the link to my blog post, it is super important than any discussion of the use of testing take into account Bayes’ Rule. The policy implications of poor quality testing being used to make decisions about reopening the economy are awful, especially if recovery does not confer immunity. If you aren’t familiar with the implications of Bayes’ Rule I strongly recommend a course of study – it’s a profoundly important concept at times like this!

  26. We are running blind without adequate testing. Lots of the arguments – like with schools and children as (or as not) vectors – proliferate because we just don’t know. We don’t know how prevalent non-symptomatic infections are or how infectious those people are. Testing and more testing and then more testing again seems needed to me – more important than tracking apps.

  27. There are reports in The Washington Post of middle aged and younger people ,positive but a-symptomatic (or almost) ,dying from a new looking kind of (brain) stroke. US medics are preparing to publish data on this. Apparently this was noticed in Wuhan too. Comparing normal death rates per location to current rates makes the overall effect of the virus bigger, in some places much bigger.

  28. At this point we do not have a reliable test, we do not have a full picture of the effects of the disease, we do not have a firm handle on how infectious it is, we do not have a vaccine and we do not have surety on how long – or if – recovered patients remain immune. Social distancing is all we have, and we can see that it works. The rest of the picture will emerge over time. If ever the precautionary principle applies, it is now.

  29. QLD is testing much less per capita than NZ.
    It seems to me we should be testing more,

    QLD and NZ have about 5m people each.
    Tests
    NZ
    24th April 6777
    25th April 5966

    QLD
    25th April,”2,095 tests undertaken in the previous 24 hours.”
    26th April 1,364 last 24 hours (could be a lag problem)

  30. Mandate masks (with some outdoor exceptions), test more, keep travel bans and social distancing. Aim for eradication.

    We should do more testing, including population testing generally and/or by sub group, eg abattoir workers, or location. I understand that even a good test can be problematic looking for small proportions, but confirmatory tests can be done, in any case % +ve is already pretty low in Qld so this is presumably manageable.

    NZ has about the same population as Qld and is conducting over twice as many tests.

    NZ
    6,777 on the 24th
    5,966 on the 25th April

    Qld
    2,095 for the last 24 hours in report dated 25th
    1,364 the last 24 hours in report dated 26th

    Australia now 35th on Worldometer tests per capita.

  31. “Herd immunity works for diseases with R0>2 if the herd is immune when the virus is introduced. That is the only way herd immunity works. “

    Ouch!

  32. Herd immunity for COVID-19 is an UNPROVEN theory at this point. The WHO has said so. My M.D. brother has also said as much.

    “WHO unsure antibodies protect against COVID, little sign of herd immunity”

    https://www.reuters.com/article/us-health-coronavirus-immunity-idUSKBN21Z2XM

    “The World Health Organization is not sure whether the presence of antibodies in blood gives full protection against reinfection with the new coronavirus, Mike Ryan, the WHO’s top emergencies expert, told a briefing on Friday.

    Ryan also said that even if antibodies were effective there was little sign that large numbers of people had developed them and were beginning to offer so-called “herd immunity” to the broader population.

    “A lot of preliminary information coming to us right now would suggest quite a low percentage of population have seroconverted (to produce antibodies),” he said.

    “The expectation that … the majority in society may have developed antibodies, the general evidence is pointing against that, so it may not solve the problem of governments.”

    For the time being relying on the herd immunity theory is a blind leap of faith or rather of rank stupidity. Please, please people stop rabbiting on about herd immunity for COVID-19. It currently has the status of an URBAN MYTH and little more. Herd Immunity does NOT happen for some diseases and coronaviruses are prime suspects for immunity “fading” and quite rapidly too. There is also the issue of mutations. Herd immunity DOES NOT happen for influenza or other coranaviruses so why do people assume it will happen for COVID-19? Ignorance, I guess. I believed it for a week or two until I researched it.

    Sweden must have had very bad advice from a seriously incompetent health advisor. They still seem to believe in herd immunity for COVID-19. So far, new data arriving are not supporting this theory.

  33. Even if recovery grants immunity, this herd immunity policy is a terrible terrible idea, for the reasons I described above. It doesn’t matter what the truth is because even under the most favourable possible scenario – recovery gives full and permanent immunity – it is still madness to pursue this stupid “herd immunity” idea of infecting a small number of people while “shielding” vulnerable people in order to get to the point where the virus can’t spread anymore.

    Epidemiologically this “herd immunity” concept is like a nationwide version of a pox party. It is absolute madness, and it will not stop the epidemic. This virus has an R0 of about 4-5, so unchecked it will grow exponentially until a large portion of the population is infected, at which point it will peak and then crash, infecting the remaining part of the population on the way down. There is no point where the % of people infected will be large enough that the virus just stops spreading. That would be true for an R0<1.5, but for an R0 of 4-5 (or even 2.5) this doesn't work.

    This stupid policy is the result of a bunch of idiots (i.e. Cummings and Johnson) looking at words they don't understand on wikipedia and making up mathematics. It has no basis in epidemiology. You do not ever allow a disease with an R0 of 4-5 to spread unchecked, because something that virulent will infect everybody. That's not a fanciful idea, it's a simple fact of mathematics. The policy is wrong and everyone needs to forget that such a stupid policy every existed.

  34. Note that there is no official Swedish government policy to aim for herd immunity. Neither was there ever an official policy to aim for herd immunity in the Netherlands. The only government who said it out load just to make a 180 degree U-turn was that British one. All well then? Well no, many including that weird Swedish big boss keep beating arround the bush about it. Even people who don´t have any explicit herd immunity plans or maybe no reflection at all but a big microphone essentially suggest that it is inevitable almost anyone will get the virus. We got an entirely unsatisfactory discourse, where it´s ok demand human sacrifice for “the economy” or “individual liberty”, but basically no one demands more stringent measures than the ones imposed by the local government to contain the virus. Opposition if it exists operates somewhere between demanding more liberties or different priorities and claiming the entire virus is a big conspiracy theory (or like the flue etc.).

  35. I am in favor of continuing the lock-down at this point, until we know more about this virus. Above, faustusnotes notes that a high R0 of 4 to 5 or more means everyone gets the disease under the so-called herd immunity strategy. I have pointed out that herd immunity for COVID-19 currently has the status of an urban myth. There is no evidence so far that it will occur just as herd immunity does not occur for influenza nor for corona-virus common colds.

    Given the continuing rank stupidity being shown by a high proportion of the human race (in countries which at least have the resources to lock-down on non-essential activities), we can say that globally this pandemic is out of control. Also, many other countries do not have the resources to lock-down properly and/or are simply too over-crowded to be able to do this effectively. Again, as I say, the pandemic is out of control globally.

    This means a country like Australia, which appears to have controlled the pandemic so far, must remain in lock-down until eradication. After that, we must remain in full quarantine from the rest of the world indefinitely until an effective vaccine and/or effective treatments are developed.

    I’ve reached the point where I have decided that this is a natural selection issue. Intelligent people will lock down as much as possible consistent with making an income or drawing a benefit. Unintelligent people will fight lock-down and go about taking more risks where they can get away with it. This will produce some selection pressure and to some extent these “stupid” genes along with genes for a poor immune system will not be passed on. Natural selection pressure, which operates all the time, will operate in this case too.

    The dangers of creating such a large infection pool include the dangers of mutation to more virulent and/or more infectious strains. Many more people could be put at risk by these fools; many of them ideologically driven fools. Perhaps we can hope that the propensity to think doctrinally/ideologically rather than ethically and logically will also be weeded out to some extent? Perhaps we can hope that when such genes are not passed on, that certain memes are not passed on also. And we can also hope that others slightly more intelligent, flexible or pragmatic can swap out in their brains maladaptive memes for adapative memes.

    This pandemic and the many climate-driven, collapse-driven events soon to occur will put high selection pressure on humans, on their genes and their memes (belief-ideas in this case). Human evolution and cultural evolution will now proceed rapidly. A time of great change is upon the human race.

  36. faustusnotes says AT 12:38 PM
    “If you aren’t familiar with the implications of Bayes’ Rule I strongly recommend a course of study – it’s a profoundly important concept at times like this!”. 

    Recommendation accepted. I did not pass until I got to – Venn diagrams and natural frequencies. And it seems doctors have a problem with probabilities ala economists and opportunity cost.

    “Visualizing Bayes’ Theorem
    Venn diagrams are particularly useful for visualizing Bayes’ theorem, since both the diagrams and the theorem are about looking at the intersections of different spaces of events.

    “A disease is present in 5 out of 100 people, and a test that is 90% accurate (meaning that the test produces the correct result in 90% of cases) is administered to 100 people. If one person in the group tests positive, what is the probability that this one person has the disease?

    “The intuitive answer is that the one person is 90% likely to have the disease. But we can visualize this to show that it’s not accurate. First, draw the total population and the 5 people who have the disease:

    “The circle A represents 5 out 100, or 5% of the larger universe of 100 people.

    “Next, overlay a circle to represent the people who get a positive result on the test. We know that 90% of those with the disease will get a positive result, so need to cover 90% of circle A, but we also know that 10% of the population who does not have the disease will get a positive result, so we need to cover 10% of the non-disease carrying population (the total universe of 100 less circle A).

    “Circle B is covering a substantial portion of the total population. It actually covers more area than the total portion of the population with the disease. This is because 14 out of the total population of 100 (90% of the 5 people with the disease + 10% of the 95 people without the disease) will receive a positive result. Even though this is a test with 90% accuracy, this visualization shows that any one patient who tests positive (Circle B) for the disease only has a 32.14% (4.5 in 14) chance of actually having the disease.”

    Diagnosing Disease

    More Examples”
    https://brilliant.org/wiki/bayes-theorem/

    Natural Frequencies as an Alternative
    (Note: Doctors’ understanding of probability seems akin to economists opportunity cost understanding; “Eddy goes on to mention an informal survey he did (of a problem that’s about to follow) where 95 out of 100 doctors mistook these prior probabilities as the correct probability as to whether a single patient’s positive result meant they had cancer.[4])

    “A proposed solution to this common misunderstanding is to represent results in terms of natural frequencies. Multiple studies, including work by Hoffrage, Krauss, Martignon, and Gigerenzer, have shown that this drastically improves Bayesian reasoning.[8]

    “Natural frequencies have shown to be a positive tool for inducing Bayesian reasoning in numerous laboratory studies,[9] the interpretation of DNA evidence in court,[10] and teaching children about Bayesian thinking.[11]

    “The issue isn’t that Bayes theorem is too difficult to understand, but in how risk and probabilities are presented. A natural frequency representation of the above problem would look something like the following:

    “Out of every 1000 women at age 40 who participate in breast cancer screening, 10 will have breast cancer. Eight out of every 10 women with breast cancer will get a positive mammography (80% of 10). 95 out of every 990 women without breast cancer will also get a positive mammography (9.6% of 990). If you have a new group of women at age 40 and look at those who receive a positive result in the screening, what percentage of these positive results do you think actually indicate that the woman has breast cancer?

    “In this case, because it’s the same problem as before, just represented differently, the answer is the same. However, in surveys, physicians were far more likely to produce the correct result with the data provided this way versus the previous way”
    https://brilliant.org/wiki/bayesian-theory-in-science-and-math/

    The Art of Risk Communication
    What are natural frequencies?BMJ 2011; 343 doi:https://doi.org/10.1136/bmj.d6386

    Gerd Gigerenzer, director, Centre for Adaptive Behaviour and Cognition, Max Planck Institute for Human Development, Berlingigerenzer@mpib-berlin.mpg.de

    “Doctors need to find better ways to communicate risk to patients

    “A 2011 Cochrane Review concluded that health professionals and consumers “understood natural frequencies better than probabilities.”1A 2011 Annals of Internal Medicine article reported the opposite, that “natural frequencies are not the best format for communicating the absolute benefits and harms of treatment”2How should physicians deal with these contradictory messages?

    “As is often the case, the contradiction lies in the definitions, not in the data. Ulrich Hoffrage and I introduced the term “natural frequencies” in the late 1990s and conducted the first studies showing that they foster understanding of the positive predictive value among lay people, doctors, and medical students.3 4 5 6 What is a natural frequency? It is a joint frequency of two events, such as the number of patients with disease and who have a positive test result, and is an alternative to presenting the same information in conditional probabilities, such as sensitivities and specificities. Conditional probabilities tend to cloud the minds of many people, including health professionals, as the following problem illustrates (for convenience, probabilities are expressed in percentages).

    Assume you use mammography in a certain region …”
    View Full Text
    https://www.bmj.com/content/343/bmj.d6386

  37. Another danger I flagged as possible may now be coming to pass. I warned that schools should not open this term in Australia (or elsewhere for that matter). I warned that we should wait until we had more data about the pathogen, SARS-CoV2, because of potential, but as of then unknown risks, to children (and their teachers). Honestly, I get tired of being “often right, seldom listened to.”

    “Coronavirus: NHS warning of rise in children showing symptoms similar to toxic shock syndrome and atypical Kawasaki Disease” –

    https://www.msn.com/en-gb/health/familyhealth/coronavirus-nhs-warning-of-rise-in-children-showing-symptoms-similar-to-toxic-shock-syndrome-and-atypical-kawasaki-disease/ar-BB13h5uz

    QUOTE

    “In the last three weeks, there has been an apparent rise in the number of children of all ages presenting with “a multi-system inflammatory state requiring intensive care across London and also in other regions of the UK”, officials said….

    The effects had been seen in children both with and without Covid-19, but there was evidence that some patients had had coronavirus previously. Professor Russell Viner, president of the Royal College of Paediatrics and Child Health (RCPCH), said parents should be reassured that children are unlikely to be seriously ill with Covid-19.

    According to the alert, which has also been shared with GPs, children affected display signs similar to toxic shock syndrome (TSS), a severe illness associated with infections, and have blood markers in line with severe Covid-19 in children. They may also have abdominal pain and symptoms of inflammation around the heart.”

    END QUOTE

    COMMENT: – Children are “unlikely to be seriously ill with Covid-19”? One, inflammation around the heart scarcely sounds benign. Two, “unlikely” does not mean “never”. If the pathogen rips through the entire community, a small percentage of a large number of children still means many ill children.

    QUOTE

    “‘Potential emerging links’

    The alert, sent on April 25, says: “There is a growing concern that a Sars CoV-2 (Covid-19) related inflammatory syndrome is emerging in children in the UK, or that there may be another, as yet unidentified, infectious pathogen associated with these cases.”

    The alert talks about atypical Kawasaki disease, a condition that mainly affects children under the age of five which can’t be prevented. Symptoms include a high temperature that lasts for five days or more, often with a rash and/or swollen glands in the neck. Children can make a full recovery within six to eight weeks if it’s diagnosed and treated promptly, but complications can develop. NHS England stressed there was no confirmed connection between Kawasaki-related diseases and Covid-19.”

    END QUOTE

    COMMENT: – As we see above, there are still many unknowns and uncertainties about these potential emerging pathologies and links. Again, we must proceed with caution and not re-open schools (fully or at all) this term. I predicted possible dangers with sequelae (downstream health impairment, degradation or death). I did not predict co-infectious behavior with another unidentified, infectious pathogen. Reality is always more complex than we predict. Our problem is our lack of respect and understandings for the potential dangerous unknowns in this pandemic.

    I’ve formed the opinion that many top government health advisors around the world are out of their depth. Their epidemiological expertise must be relatively low. That is clear from their slow, uncertain and vacillating judgements and reactions. Their understanding of complex system emergence must be even lower and their awareness of black swan events with “fat tail risk” (see Nasim Taleb) and what that means must be non-existent. These supposed experts are not nearly expert enough.

    Clearly, pandemic management stands in as much need of an intellectual revolution as does economics.The old atomistic understandings of simple, single path causal chains and one to one relationships must jettisoned in favor of network thinking and emergent and evolutionary thinking which do not fail to the simple fallacy of composition.

  38. akarog,

    I am aware of that. The arrival of a pandemic disease, our unpreparedness for it and our exposure to “fat-tail” risk in this regard were all predicted by Talib, Gates and many others. It was even long expected by me since I read a book in the early 1990s called “The Coming Plague”, meaning a coming plague of zoonotic diseases plus new flus (which itself was originally a zoonotic disease). I have a medical science acquaintance who predicted this day would come in the 1980s. Although he expected most likely another killer flu. Talib is smart but he did not figure this stuff out. It has long been known. He may have made some innovations in the theory and math of risk. I am not knowledge enough about his work in those fields. He seems a very good complex system thinker too.

    What was a black swan, in a sense, was the precise nature of the disease and its interactions with human biology and human socioeconomic systems. Because one predicts with great accuracy that a bomb will blow up, that does not mean one can predict where all the pieces will fall in a complex chaotic system environment. Maybe even with other devices going off nearby at about the same time. I am sure the “three explosive device” problem is a lot more complex than the three body problem. (i’m not talking about shaped charges strategically placed for demolition.)

    We have a number of environmental “explosive devices” going off right now and at close to the same time in historical terms. Global bush-fires and other climate change effects, plus the sixth mass extinction and now an open-ended pandemic on humans, to name just three. Then there is the over-interconnected fragility of our global economic system and the mess of another global finance, asset, and wages collapse happening, or about to happen right now.These are the death throes of the Capitalist system and maybe even of the West.

    China and the absolutist CCP will come out of this crisis extraordinarily powerful and probably the sole economic superpower of the world. The only check on them will be the knowledge that the USA has a lot of nuclear weapons and are definitely crazy enough to use them if pushed. This is unless we adopt democratic socialism. If we do not, we (the West) will completely crumble and collapse. The empirical proofs have arrived that capitalism is unsustainable. I have long predicted this as have the thinkers I read.

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