Social Distancing Works

First, the bad news.

The death toll from Coronavirus in the U.S.A. stands at 4,059, and more alarming is the fact that yesterday brought nearly a thousand deaths in a single day. The numbers keep rising.

America has confirmed 188,639 cases (many more unconfirmed), more than any other country in the world (although Italy leads in fatalities with 12,428). The total number of cases in the U.S. shows a very unfortunate and frankly, scary trend: exponential growth.

Exponential growth definitely does not follow a straight line — not even close. But if we plot it on a logarithmic scale, it does — at least approximately. That is the nature of exponential growth.

Now some good news.

The earlier numbers are quite small, which makes their random fluctuations relatively large, and they are plagued by uncertainty of detection and reporting, even more so than recent data are. So, I’m going to focus at what has happened since March 5th, 2020. I’m also going to look at the number of new cases each day, rather than the total number of cases. If I graph that data, I get this:

If I graph it on a logarithmic scale, it looks like this:

The good news is that the number of coronavirus cases doesn’t follow a straight line exactly, not even on a logarithmic plot. What that means is, that it’s not showing “exponential growth” exactly — at least, not at a constant growth rate.

That departure from straight-line behavior isn’t just random fluctuation. It can be statistically verified, and even quantified. Here is one good statistical model, consisting of two straight-line segments representing two different growth rates:

The growth rate of new cases seems to have slowed around Mar. 23rd (give or take a day or two), with the result that it has reduced the number of cases we would have had lately. By a lot. The red arrow above shows where we would have been yesterday if growth had continued at the same rate; clearly there are fewer cases with the newer, slower growth rate.

The difference may not seem so impressive on the above plot, because it’s on a logarithmic scale. Let me show you what it looks like on the usual kind of plot (just the numbers, please)

At the previous rate of increase, we were on track to have more than 100,000 new confirmed cases yesterday. Thanks to the reduced growth rate, we only confirmed 24,742. Our health care system is already burdened by the cases we have now. Imagine how bad it would have been if, insteading of dealing with 24,742 cases, we had to handle over 100,000.

Why did the growth rate decrease? There are many possible reasons, and many factors, but my hypothesis is that the primary driver has bee social distancing and protective measures (handwashing etc.). [Caveat: I am not an epidemiologist.] People may feel their efforts are in vain, contributing little if anything to help. But by slowing the spread of the disease, we give our already-overworked health care system more time to cope. Previously, new cases were increasing at 29%/day; now they’re going up at a much slower rate, only 11%/day.

And that means more lives saved.

So — congratulate yourselves. You are the ones who made this possible, who made it work. Social distancing and protective measures are NOT in vain.

These things work. They save lives. They already have. Don’t stop now.

Thanks to everyone who helps slow the spread of the disease. If you’d like to help support this blog, please visit the donation link below.

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82 responses to “Social Distancing Works

  1. Christine Shepard

    I was hoping you would do a post on this.

  2. How do you know it’s not just this a lull instead oof flattening? The USA has multiple hotspots that appear potentially to be on the cusp of happening at the same time.

  3. Vitamin D is being left out of the discussion. The sunshine vitamin has many roles in our bodies. Enhancing some specific aspects of our immune system is one of them. One scholar of vitamin D considered colds and flu to be signs of vitamin D deficiency. A blood level of 50 ng/ml or higher is needed for vitamin D to perform its immune functions optimally. Most Americans are deficient this time of year.

    For a quick basic education on vitamin D and it importance in immune function read “Epidemic Influenza and Vitamin D” by Cannell, Vieth, and Giovannucci . It is posted on the National Institute of Health website.

    • Bullshit.
      Vit. D has plenty of positive effects in regulating our immune system but there is NO evidence that it has any kind of significant or practical beneficial to tackle the existing COVID-19 pandemic at individual or population level.
      This is pure bullshit that diverts attention from the key factors we already know actually work: social distancing, good quality hand washing, curbs on people movements.

    • Vitamin D will certainly not have been the reason for the change point. It is a fat soluble vitamin and humans have a lot of fat storage capacity. And it would go in the wrong direction with less people going out.

      Vitamin D begin too low at this time of year will also not be the reason for COVID-19. The Chinese had the problem 3 months ago.

  4. JCH,
    The best way to tell that it is real is:
    1) Testing and reporting were more likely to be low at the beginning of the epidemic than later on.
    2) The deviation you see is greatest in the most recent days
    3) This has all been due to the efforts of mostly blue-state governors (Larry Hogan here in MD has done a good job as well). States like TN, MS, AL and TX are still quite exponential, albeit mostly on the early part.

    The curve is flattening–it’s even clearer in S. Korea and in the latter portion of the epidemic in China.

    • South Korea is two stories. One was a secretive religions sect that recruited young people. The initial outbreak was there. Because of their practices, the outbreak in that sect was fast and furious. The public health workers instantly had all their names, addresses, phone numbers, and email addresses, so tracing contacts, testing, isolating, etc. was unusually effective. South Korea admits this. The other outbreak is in their general population, and it is developing very slowly, but it is developing.

      I think China flattened their curve – a very very slow growth in new cases. Nobody else has.

      • The point is the S. Koreans were on this like a bad suit on a tall man. The source of the infection is of limited importance–what matters is how it propagates afterward.

        [Response: I hope everyone pays attention to this comment.]

  5. I did some comparable calculations for Germany. Actually, with a little bit of finger crossing and handwaving, one can calculate the reproduction number at a point in time the “registration lead time” (RLT) ago. The latter being the mean number of days between infection and oficial registration. With the somewhat courageous assumption of people not infecting others after their registration – due to isolation – all new infections must origin from unregistered infected. So I can calculate the ratio for each day and sum this up for RLT days to get the total number of infections caused by one infected.
    This is the link to the page Google Translation is a bit awkward, but it should do the job. The google spreadsheet unfortunately seemingly cannot be translated:
    A similar logic can be applied to calculate the mortality of registered cases, which is currently around 4,5 % here.

  6. Beautiful work, as always. Thank you!

  7. I’ve been looking forward to your comments on some of this and am grateful to see it most especially as it shows you are alive and well. I wish the same for all your friends and family.

    Would you please comment on the validity of conclusions concerning how deadly COVID-19 is considering the low levels of testing in many areas combined with the fact that many people who get it will have no symptoms?

  8. Reblogged this on hypergeometric and commented:
    Nice work by Tamino, including showing when a log plot is appropriate and when it is not.

  9. Jim Prescott

    What do you think of the visualization approach taken by (and documented in the accompanying minutephysics video)?

  10. It all depends on trusted data collection – China suddenly lost many of millions of cell phone subscriptions. Other data sources point to serious doubts on their numbers

    • That video is a questionable source at best. Moreover, it’s not possible China is hiding “massive” numbers of cases. First sharing of information between Chinese medical scientists and U.S. and European scientists were informal, and now we have a bucket of publications studying their outbreaks for lessons learned, etc. See LitCovid and check out from where most of the authors hail. If there was a substantial hiding of cases, statisticians (like me) would detect it because we are naturally suspicious of everything we are shown. There are tests to detect suppression, too.

      In fact, contrary to many storylines, the Chinese medical scientists are heros, because, despite the opposition of their local region’s leadership, they went public anyway. It’s because of them, for example, that we got samples and sequences of the RNA of the virus. The first preprints of articles about it showed up about mid-late January, and there was increasing collaboration as chronicled in history at the preprint server. Peer reviewd articles from China appeared beginning in early February.

      It was already clear this virus could be dangerous, given comparisons with SARS, and the Chinese were already assembling catalogues of approaches to try to contain it. But facts are it was completely new, and no one at the time understood how horribly contagious it was. But everyone with knowledge was worried.

      Meanwhile, and this will be the story of the medical and government failure in Europe but especially in the United States, we did nothing because it was “over there”. And the U.S. government had guidance and a playbook on how to respond, which was ignored.

      Given how piss poor U.S. government response was, as Don McNeill, Jr recently suggested, a logical and rational thing for the U.S. to do would be to ask China for doctors, supplies, and help.

      • Thanks for some rationality ecoquant. There is a weird (almost entirely US-based) ‘blame China/it’s all a plot’ meme, when so far as I can tell from here they’ve done a better job than nearly everywhere else (modulo the initial suppression), and have been very good at passing on what they learned to medics and researchers elsewhere.

    • In Hubei approximately 35,000 people die of various causes each month and have to be buried. The Province was shut down for weeks. I do not know whether or not they continued to process bodies through cremation the entire time, but it’s very possible they did. One hint, many of the people who were in line were interviewed and they said they were there to pick up the remains of their loved ones who died during the lock down, and one even said their loved one died of natural causes. So if they waited 4 weeks to process, there could be 38,300 bodies to process all at once.

      Regardless, before people accuse them of covering up “40,000” dead, maybe they should ask first.

      • And all this China bashing is oddly reminiscent of false stories in the media by our government in the past:

        1. weapons of mass destruction
        2. weapons grade powder proved Saddam made the anthrax
        3. yellow cake
        4. Saddam’s soldier smashed the heads of babies in a hospital nursery on its tile floor

        Stinks like that.

        The explained their data gathering in papers published in journals. They told the world on January 29 that pre-symptomatic transmission was suspected.

  11. Can you do any improved analysis on the confidence of this, based on testing estimates only showing 15-18% of cases actually being reported in the US currently? (Reference:

  12. And, no, I won’t believe a report from the U.S. IC regarding many more deaths in Wuhan until they reveal methods and sources and permit an independent verification.

    • They were claiming the anthrax was in a powder that was so fine it had to be weapons grade, and that sinister fact made it certain Saddam made it. It sounded plausible. War! This went on in the media for several days. One day they said a micron size, and the name of the substance it was made from: bentonite. The technology! Military grade! I don’t know jack about anything, but they mined that stuff where I grew up. I found the name of the company that did the mining and they had a website where any Tom, Dick and Saddam in the world could buy it by the bag, and in much finer microns than the stuff in the envelope that was supposedly specialized top secret weapons grade. So that night I put links to that website catalogue all over the internet, and the DC/CIA crowd and their NYT’s culprits dropped “weapons grade power” like a big rock.

      I swear the NYT’s, and now Bloomberg, will print anything they are told to print when DC wants to spread lies. They’re like lie cheerleaders.

  13. Reassuring to know you are out there tamino thanks for the post .

    Korea has probably the most accurate numbers as JCH has touched on.
    They had tested 275,000 people as of the 17 march and have kept up the effort since. This was not testing just symptomatic cases and I assume they have included asymptomatic cases in their case count
    From their statistics we can get three estimates of the fatality rate .
    Total Cases: 9,976 Deaths: 169 gives 1.69% death rate
    Resolved cases 5997 to deaths 2.82% death rate.
    Using cases two weeks ago to deaths now to allow for the delay between diagnose to death gives 7024 cases 16 march to 169 deaths 2.41% death rate.
    Data from world meter .
    Frankly terrifying.

    Stay safe all. Keep your distance and please be kind .

  14. I know it’s a bit off-topic, but I just wanted to mention something Tamino, in case he hadn’t already heard about it. The China Meteorological Administration (CMA) recently published their China Merged Surface Temperature analysis (CMST), a global surface temperature trend analysis:

    “A new merge of global surface temperature datasets since the start of the 20th century”

    Data here:

    It looks like CMST under-estimates warming in the Arctic in comparison to NASA’s GISTEMP (see figures 9c and 10), though the CMST authors take this to mean that GISTEMP over-estimates Arctic warming. Of course, that’s wrong. For example, a comparison of GISTEMP to ERA5 and AIRS dispels that notion:

    page 11 of: “NOAA/NASA: Annual global Analysis for 2019”

    Click to access 20200115.pdf

    Still, it doesn’t look like CMST under-estimates global warming as badly as the Japan Meteorological Agency’s (JMA’s) analysis, given JMA’s very sparse coverage, including in the Arctic.

    Also, I’m pretty sure the NCEP-2 re-analysis shows global surface warming acceleration, based on comparing its 1979-1999 trend to its 1999-2019 trend. A more formal analysis would likely confirm that as well:

    And HadSST3 under-estimating recent sea surface warming in comparison to HadSST4 likely explains why Cowtan+Way, HadCRUT4, and Berkeley Earth don’t show warming acceleration. There’s also likely a contribution from HadCRUT4’s poor coverage (especially in the Arctic), along with Berkeley Earth slightly under-estimating Arctic warming. Finally, COBE-SST under-estimating sea surface warming in comparison to COBE-SST2 likely explains why JRA-55 does not show warming acceleration either. I have a multi-tweet thread covering those issues:

  15. Some autocorrect made “Where we were headed” into “Where we were header” twice on your charts.

  16. The ‘single bend’ deviation from ‘exponential’ seen in the US rate of Covid-19 infection is not seen as a ‘single bend’ within the Covid-19 data of the various European countries. They (that is Italy, France, Spain, Germany, UK) show curved deviations (although with differing curvature) lasting so-far a month or more, this despite the distancing/lockdowns occurring as singe national events.

    • At least in Germany people were already doing a lot voluntarily before the government sharpened the official rules to make sure also the last dumb/egotistical people collaborated. I am personally not even sure whether these rules were necessary, we need to bring the average number of close contacts down, the last few percent is not that important, but video and photos of these dumb people gathering created a lot of media attention.

      So the day the rules went into effect, except for closing schools and shops, likely did not do that much anymore. We did not have head of state calling COVID-19 the flu, so people took action early on.

  17. US reported testing has slowed and plateaued around 100K tests/day, (with ~15% positive, so it limits the growth to additive +15Kcases/day rather than a +20%cases/day +33%cases/day exponential.

    See the graph on for the plateauing.

    Or get their testing stats from the dataset at

    • Looking at the last several days from the spreadsheet, the last several pos+neg tests the US’ has completed are these

      117,698 4/2
      100,989 4/1
      104,117 3/31
      113,503 3/30
      95,647 3/29
      109,037 3/28
      107,329 3/27
      97,806 3/26

      The testing is clearly not growing exponentially.

      The percentage of positives have come up from 10% to 18%, probably because they are restricting the testing to the most serious cases.

      The limited testing as the testing does not scale up with the spread is likely having a larger effect on the growth of detected cases than the social distancing. In any case, the slow testing is hiding some of the effect.

      • Making a prediction from yesterday’s testing numbers, US cases of 239,009 on 4/2 (per spreadsheet) will increase 117698tests/day*1.15*0.188pos/test=25446pos/day to make the 4/3 number of confirmed cases be less 239,009+25,446=264,445 confirmed cases, or a maximum % increase of around 10.5%.

        This assumes:
        * 15% tests/day increase, (far above the 3%/day average increase of the last week). Since there seems to be some moving-average effect on tests completed, this could be far lower than 15%, but there are hints that new tests are beginning to come online.
        * 18.8% positive testing results (4/2’s result and the highest value in the series). This I expect to go up, as we continue to triage the allocation of testing. Somewhere on the wild internet, I saw someone say that we’d need to be testing at a level that produces a 15:1 ratio of pos:neg or get the positive result rate down below 6.25% to get things under control. That would mean testing at at least 3x as much (running 350K tests/day) today, and be increasing that at at least the rate of spread of the disease.

        Since testing seem so limited, I’m very skeptical that social distancing is the main cause of the lower growth in reported confirmed cases.

      • Prediction-wise, I underestimated the 271,915 US confirmed cases by 7470 cases or 2.7% per the spreadsheet.

        The good news is that US testing capacity grew by 17.5% over yesterday to running 139,613 tests/day. That’s the best improvement in capacity we’ve seen in a week.

        The bad news is that the % positive also grew to 19.3%, indicating we’re testing an increasingly sick pool of people.

        Together, they added 32,906 new cases to the total, or 13% growth.

        Carrying these simple-minded trends forward for 4/4 would give 139,613*1.175*0.193=31,661 new cases for tomorrow, or 303575 total confirmed cases, or an 11% growth.

        Still, I think the US cases have been bound more by the limited testing than by dramatic decreases in the spread of the disease.

      • @DRF5N,

        Do you know in your dataset how the ratio of positive tests to sum of positive and negative tests has held up over time? I looked at that briefly, but for other reasons.

      • Prediction-wise with 303,575 for 4/4 I underestimated today’s 305,755 US confirmed cases by 2180 cases or 0.7% per the spreadsheet.

        The very good news is that the numbers show US testing capacity grew by 55% over yesterday’s 139,613 tests to running 216,539 tests/day. That’s the best %improvement in capacity we’ve seen since 3/18.

        The mixed news is that the % positive dropped to 18.8%, indicating we’re testing a slightly less sick pool of people. But a big part of the increase in tests was clearing about 45,000 cases of backlogged tests in California. See Because of the backlog-clearing, keeping up the testing rate at 216,539 or the 55%/day growth in testing capacity might be difficult.

        Together, they added 33,840 new cases to the yesterday’s 271,915 to make 305,755 or 12.4% growth.

        Carrying these simple-minded trends forward for 4/5 would give 305,755*1.356*0.188= 77945 new cases for tomorrow, or 383700 total confirmed cases, an 25% growth. (Note that the 1.356 factor isn’t the 1.55 increase–I noticed my sloppy, back-of-the-envelope spreadsheet has been using the 2-day moving average growth. I was looking at the 2day average to smooth out what looked like tests not being reported by the cutoff one day being made up the next &vv, and that’s what I’d poked that into my estimate calc)

        Since this naive model of the testing process dynamics has done so well, I am increasingly and depressingly convinced that the US case numbers have been bound more by the limited testing than by dramatic decreases in the spread of the disease.

      • 138,243 0.188591697170909

        Prediction-wise with 383,700 for 4/5 (303,575 for 4/4) I dramatically overestimated today’s 332,308 US confirmed cases by 51,392 cases or 15.4% per the spreadsheet. (I just noticed I made an important typo yesterday, multiplying the total cases instead of the testing capacity. I should have posted 216536*1.356*0.188=55201 Oops. )

        The good news w.r.t. my prediction is that it is a big change in the new cases trajectory from yesterday. And that with 26,553 new cases, there were 7,287 less new cases reported than yesterday’s 33,840 new cases.

        The bad news is that at 138,243 completed tests, we reported 78,293 less tests compared to yesterday’s 216,536 tests, and more than a thousand less tests than the day before’s 139,613. % positive stayed the same at 18.8%, indicating we’re testing about the same pool of people. See Because of yesterday’s backlog-clearing, keeping up the testing rate at 216,539 or the 55%/day growth in testing capacity didn’t happen. The folks think ~140k is

        Together, they added 26,553 new cases to the yesterday’s 305,755 to make 332,308 or 8.6% growth.

        Carrying these simple-minded trends forward for 4/6 would give 138243*0.995*0.188= 25860 new cases for tomorrow, or 358,168 total confirmed cases, a 7.8% growth.

      • Not sure this is threaded correctly, even after repeated scrolling, but I want to thank smallbluemike for explaining further his comment about initial viral load and disease severity.

        While I think my mental model of the process still makes sense, I only considered viral ‘inputs’ up to a million. If I think about mike’s examples–ER workers on shifts with no PPE, or a 60-person choir singing together in an enclosed space–it seems intuitively likely that the resulting intake of viral particles could go far beyond that range. If so, then yeah, the idea of really massive ‘inputs’ swamping the immune system hopelessly make sense. (So, perhaps, does the possibility of ‘over the top’ immune responses proving pathological in such a circumstance–for example, inflammation has its benefits to the body, which it is part of our evolved response repertoire, but quite often it causes problems, too. Speculating…)

      • Thanks for the article, mike.

    • The US confirmed covid case number is artificially reduced by the fact that even patients with symptoms can’t get tested easily. Our testing regimen is not very similar to that of South Korea and others that come up in comparisons. The covid number to watch in the US is the number of deaths. It’s hard to reduce that number by artificial means or incompetence. People die and their deaths are certified with a cause of death. Number crunchers may be able to approximate the number of actual cases in the US by working backward from the number of deaths, but the US confirmed case number is a bit of an outlier for global comparison because of the Trump testing fiasco.

      • But the death rate is about 8-15 days behind the infection rate.

      • The death rate from Covid 19 is going to be understood in retrospect in the following way: Your chance of death will be increased significantly if your initial exposure to the virus is large. A small initial exposure to the virus is going to be less deadly because the small initial infection gives your immune system an opportunity to spot the invader and start working on an immune response. The exponential growth of the virus simply charts out to be overwhelming if the initial dose is large. This isn’t going to be the only takeaway on the mortality issue, but it will be an important issue in the deaths of people with no underlying health issues or the other risk factors that suggest a higher mortality rate would be expected. An initial large dose is quite dangerous and sometimes deadly.

      • at snarkrates: yes, death lags 8 to 15 days behind infection. But the rate of death will be amplified as the initial exposure dose rises. Need data: look at death rates of ER and emergency response workers who encountered the virus with insufficient PPE.

      • @SmallBlueMike,

        One way to estimate prevalence is to look at ratio of deaths to sum of deaths and recovered.

      • @eq yes, there is a lot of room for calculation based on C positive deaths, C positive recoveries, etc. I don’t think any of that helps us managing the pandemic very much. Once there are confirmed cases in a community, there are likely many unconfirmed cases as well. This means the virus is spreading in the community already. We know what to do about that: lockdowns, quarantines, etc. What we cannot do is effective suppression based on effective widespread testing and contact tracing. That ship has sailed. We are on our heels now in the US wrt to this Coronavirus. I will continue to make myself scarce in public space and wait it out.

      • That ship has sailed. We are on our heels now in the US wrt to this Coronavirus. I will continue to make myself scarce in public space and wait it out.

        As are we, and most we know. As is my son in NYC. My only “violation”, although it preceded any official guidance, was a visit to my younger son and his wife in London, 26 February through 3 March.

        Best wishes, luck, and health to you and yours. And same, in fact, to everyone in the Tamino discussion community.

        The Spiegelhalter assessments are reassuring, but the news and lack of competence at the top is pretty stressful, especially for those of us who are more senior and have a couple of conditions.

      • The death rate from Covid 19 is going to be understood in retrospect in the following way: Your chance of death will be increased significantly if your initial exposure to the virus is large.

        Got any support for that idea? I’m skeptical, because of this line of reasoning: it seems to me that by the time you get to the symptomatic stage of infection, you’ve experienced many, many doublings of the virus load. However, starting from one particle, it only takes 10 doublings to get to 1,000 particles, and just 20 doublings to get to 1 million particles. And I don’t know, but I suspect that even a million virus particles probably aren’t provoking much immune response–yet.

        Therefore, I think initially getting 1 particle, versus getting 1 million particles, probably doesn’t make much difference. Some difference, sure, since you’d have to think that 1 particle has a finite chance of getting killed off without propagating, and that chance must go down the larger the initial load. But I really doubt it would affect the seriousness of cases that do develop; it would just reduce the probability that a case would develop.

      • at Doc Snow: “Got any support for that idea? ”

        Some. Here:

        “It is early days, but if the initial amount of virus a person is infected by doesn’t correlate with the severity of disease symptoms, this would mark covid-19 out as different from influenza, MERS and SARS.

        For influenza, a higher amount of virus at infection has been associated with worse symptoms. It has been tested by exposing volunteers to escalating doses of influenza virus in a controlled setting and carefully monitoring them over several weeks. This hasn’t been done with covid-19, and is unlikely to happen, given its severity.

        Animals infected with higher doses of the SARS and MERS coronaviruses also experienced worse outcomes, says van Schaik. “I think we just have to conclude that while this virus is related to SARS, there are also important differences that are currently poorly understood,” he says.

        Even if the initial level of virus at infection isn’t related to disease severity, it still pays to try and minimise our exposure to the virus because this will reduce our chances of falling ill in the first place. “We want to be taking every precaution we can to prevent ourselves getting infected, which will also reduce our ability to pass the virus on to others,” says Parker. “Any measures we can take to avoid infection are worth taking.”

        The conventional wisdom about covid 19 has been evolving on an almost daily basis as the real science catches up with the true dynamics and parameters of this virus’ means of transmission, etc. The trend in the evolving wisdom has all suggested to me that we should err on the side of caution and that would include trying to minimize the dosage of initial exposure if possible. It is not rocket surgery to figure out how to do that and it won’t create significant additional hardship. If you want to go the other way and hang out with a choir singing in an enclosed space, you are free to do so. There is anecdotal evidence to suggest that could be a mistake:

        Think about the respiratory mechanics of approx 60 people singing in an enclosed space. Cogitate about the viral load that probably built up in that space (where no one was coughing or sneezing or otherwise symptomatic), then reflect on the fact that within 21 days, two of the participants were dead. That seems like a statistically unlikely rate of mortality for the circumstance. It was certainly a surprise to the choir folks who acted on the conventional wisdom available to them on March 10th. Is this definitive? No. But I can read the handwriting on the wall and I will err on the side of safety and do what I can to avoid exposure. And to minimize the dosage of any exposure that I might bump into. People running and biking by me, huffing and puffing? No thanks. I understand the dynamics of aerosol and droplet expulsion enough to want to avoid that. Go in a sacred, enclosed space and do a bit of singing with other folks who all appear healthy? No thanks. That’s not a risk I need to take. If you want to run a very small number experiment on the risks of high initial dosage, we can do so. I am happy to work on the group that cranks out data based on low initial dosage based on the factors and actions that are available to us. I was out this morning for a brief essential errand in WA State in enclosed space. I was the only person wearing a mask and carrying hand sanitizer. Even at this late date in the infection paradigm at work in WA State, I want to give my immune system all the help I can to enable it to respond effectively to covid 19. But there were a half dozen folks in that space while I was there, maintaining a “safe” social distance, but not wearing masks. We wear the masks to protect others. To demonstrate responsibility. Is this hard to understand?

        The two people behind the counter? No masks, but they were still rattled by the an event from earlier this week: a car had pulled up out front this past week and the driver’s foot had slipped off brake and on to the gas pedal. Took out one of the doors and a window before car stopped in the lobby. That was quite a scary event. The steady stream of customers with no masks? Not so scary. Any hand sanitizer on the counter? Only the one I brought, used and left with. They did have portable tables set up in front of the counter to force a little distance.

      • I don’t have a reference but I did recently read an article about viral load and apparently it has been known for some time that the viral load at infection is very important to the severity of the illness that follows. Covid-19 is unlikely to be any different so, for example, face masks for all could help reduce the severity of this pandemic.

      • That the viral load of the initial exposure would influence the severity of the disease makes sense, given that the virus is in competition with the immune system and the way the virus targets the lungs. If the initial exposure is high, it can get out of hand before the immune system can deal with it.

    • There is also an issue with how the tests are being administered. Evidently, the swab has to be inserted quite deep into the nostril, and so about 1/3 of negative results are positive.

      • Do we have enough data to know/use that yet? It all seems like a big CF rife with opportunities to fall short of the best case scenario.

      • The US testing process is a pretty comprehensive catastrophe. There are so many things wrong with it that it’s hard to know where to start. Too late to fix this now because the virus is out and contact tracing can’t be very effective once your testing procedure falls on its face at the starting gate.
        I think the US needs to move on to the antibody testing now. Maybe we can get that right. There is not as much urgency on that because US citizens now need to be in lockdown until epidemiologists (Dr. Fauci?) says we can ease the lockdown. I think positive antibody testing might allow some folks to come out of lockdown safely. These folks should still observe social distancing, handwashing, etc. Presence of the antibodies would not mean that the person could not infect others, only that a person with antibodies may be at lower personal risk. I will wait for the science to catch up and develop solid protocols for recovery from pandemics in general and this pandemic in particular.

  18. Released today in Science, open access for the duration of the pandemic:

    * L. Ferreti, et al, “Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing”, March 2020
    * An investigation of transmission control measures during the first 50 days of the COVID-19 epidemic in China

    The linked articles also each have supplementary files for them, which summarize data sources and provide greater detail.

    • Sorry, left off the lead author for the second paper … It was Huaiyu Tian of the State Key Laboratory of Remote Sensing Science, College of Global Change and Earth System Science, Beijing Normal University, Beijing, China.

    • Mal Adapted

      Thanks DBB, that is a good read.

      The author is Ed Yong, a well-known science writer. The short take is that because pre- or asymptomatic carriers can apparently spread the virus by talking or just exhaling, we should all wear masks to avoid transmitting it even if we’re not sick:

      If people are infectious before they fall sick, then everyone should wear face masks “when going out in public, in one additional societal effort to slow the spread of the virus down,” says Thomas Inglesby of the John Hopkins Center for Health Security.

      For that purpose, even a homemade mask is better than none:

      A few studies suggest that homemade cloth masks are less effective than proper medical ones, but are still better than nothing. In one experiment, a surgical mask filtered 89 percent of viral particles from the air, a tea towel blocked 72 percent, and a cotton T-shirt blocked 50 percent…remember that homemade masks are not fully protective. They’re a last-ditch measure to be used in situations when social distancing isn’t possible.

      Accordingly, while I don’t think I’ve been exposed to the virus yet, I wore a disposable dust mask I had on hand when I went to the grocery store yesterday. I didn’t wear it when walking in a local park, but did step off the trail when necessary to maintain adequate social distance, while exchanging pleasantries with the other walkers. It might be more considerate not to speak, but only nod and smile ruefully 8^}.

      The author also points out a less obvious benefit of masks:

      In Asia, masks aren’t just shields. They’re also symbols. They’re an affirmation of civic-mindedness and conscientiousness, and such symbols might be important in other parts of the world too. If widely used, masks could signal that society is taking the pandemic threat seriously.

      Good stuff.

  19. When did the idea of social distancing come to the US? There would likely be a, roughly, two week lag between any measures and the effect of those measures, since it can take up to two weeks or more for symptoms to appear. This seems to be the case in Italy where it took nearly three weeks for the figures to start having a discernible effect on the case number growth. However, “discernible” is not statistical test, just a guess. So it may be that social distancing had a more immediate effect but I would have severe doubts. two weeks before March 23rd, the US had only 704 cases and Trump would have been at peak denial.

    • I’ve been computing the daily increase in reported cases since March 15th. It’s an ugly format, but here are the daily results to yesterday (4/3/20):


      As one can see, there’s been a monotonic fall since the bolded figure (March 26th–also, ironically, the date the US surpassed both China and Italy to become Covid Central.) Two week prior to the 26th would be the 12th–and, coincidentally/anecdotally, my work officially evaporated due to quarantine measures on the 13th. Other restrictions came into play on the 15th. So I think that the figures are consistent with the lag you mention.

      As to drf5n’s idea that the flattening of the curve is due to the limitations of testing, I’m a bit skeptical, though I have to respect what I’ve seen of his work. From what I see–and I’m in South Carolina, which is still not locked down despite many calls to do so–everyday behavior has changed quite a lot. If it weren’t having an effect on caseloads, that would also demand an explanation!

      • doc says: “As to drf5n’s idea that the flattening of the curve is due to the limitations of testing, I’m a bit skeptical, though I have to respect what I’ve seen of his work. ”
        Mike says, wait and see. I have been attempting to get a test for weeks without success. My daughter with symptoms similar to mine, but a bit worse, did manage to get seen at a drive thru urgent care clinic today. The drive thru clinic diagnosed strep and sent her home with strep meds, but they did not do a covid test and remarkably, they did not do a strep test either. My dtr is an adult, but she is also my child and I am livid about this poor quality treatment. My sense is that drf5n is correct, but we will have to extrapolate backwards from deaths or other somewhat definitive measures. The US testing fiasco is very, very bad. Even now, at this late date, it might still be useful at reducing infection levels and testing is still effectively not available for that purpose, it is only being used now to identify the sickest covid carriers. What a mess.

        fwiw, I have three daughters. One died in 1988 as result of botched surgery and lackluster post surgical care. I do not want to survive any more of my children or grandchildren. That shit is excruciating.

      • @DocSnow. To be clear, are those numbers thousands of new US confirmed cases, (i.e. positive tests)? Perhaps from the spreadsheet?

      • drf5n–Sorry about the delay in responding; been busy with other stuff. But the source is the Worldometer tracker:

      • sbm, my heart goes out to you wrt your daughters. And I agree completely that “The US testing fiasco is very, very bad.” I actually just wrote about that here:

        Apparently, the US public isn’t being informed very clearly about just what the testing situation actually is–unlike the Canadian public, for one instance. And more than apparently, the fumbling of the testing at the beginning of the epidemic was criminally negligent. Can’t sue, I think, due to sovereign immunity. But this Maladministration needs to pay in full at the ballot box this fall.

  20. A little note from the White House on how to do science and prediction of the future from models properly:

    “A White House representative said the task force has not publicly released the models it drew from out of respect for the confidentiality of the modelers, many of whom approached the White House unsolicited and simply want to continue their work without publicity.”

    Words fail me.

  21. Forgot to mention: This was in relation to the prediction of 100,000 to 240,000 deaths from coronavirus.

  22. @jgnfld,

    What kind of statistical modeler refuses to share data, derivations, assumptions, and code?

    That’s worse than I thought. I say the results are, as a consequence, completely untrustworthy, and actuals could go anywhere, per Boice and Wiederkehr’s article below.

    BTW, adding to the pile of references and sources, the two articles at Five Thirty Eight about why this is so hard are good:

    Politics Podcast: Why Forecasting COVID-19 Is Harder Than Forecasting Elections

    Best-Case And Worst-Case Coronavirus Forecasts Are Very Far Apart

    • The bizarre thing to me is this.

      While riding herd on some high schoolers on March 13–it turned out to be the last day I, or anyone else in Kershaw County, SC, would work as a substitute teacher–I punched out the scenario of a constant 30% daily increase in reported US cases, using a sheet of notepaper and a beat-up school calculator. (The 30% was an empiric ‘simple estimate’ based on the then-recent history, and biased to be a bit conservative.) The result indicated that on March 29 the US would have 110,991 reported cases.

      On March 15-16, a group of professional epidemiologists was polled about the probable course of the epidemic in the US:

      At the time the survey was in the field, about 3,500 cases had been reported. But the experts estimated that by Sunday, March 29 — a little under two weeks after they took the survey — the country would have seen anywhere from 10,000 to 75,000 cases… The consensus forecast generated by the individual responses indicates that we should expect roughly 19,000 reported cases by March 29, with an 80 percent chance of seeing between 10,500 and 81,500 cases.

      (Actually, there was one outlier, who projected anywhere from 10k to 500k cases–which is a range so large as to be fairly pointless. Presumably that person just didn’t want to say “I have no idea.”)

      And the reality?

      On March 29, per the Worldometers tracker, which features a fixed update at 0 hours GMT, the US had 142,178 cases–roughly 2 day’s progression ahead of my scenario, but roughly double the 75k upper bound given first in the quote above.

      The question isn’t “Why did I do relatively well?” The question is “Why did the professionals do so abjectly poorly?” Their modeling was surely much more informed and sophisticated than mine. Can it be that those very factors introduced unnecessary uncertainty, and permitted play to emotional biases that made the analysts reluctant to accept how bad things could get, and how fast? I really wonder.

      • Nic Jewell, a statistician and mathematician at MSRI gave a talk about SARS-CoV-2 and its disease:

        He introduces SEIR models and the lot, and also talked about how it is so difficult to use them for projections, something which FiveThirtyEight did a decent job at explaining recently. (Not so much Silver’s recent numerical op-ed about why case counts are meaningless.) Being an empiricist, Jewell suggested that if you wanted to see where any (“typical”) country (or region, for that matter) would be with the disease, you could find where their number of deaths per day lined up with, say, Italy’s, and call that a matching day.

        Then, just look at where Italy’s number of deaths per day are forward and that’s the prediction of the regions.

        Obviously, the U.S. has a much bigger population, so there are limits to this technique, but …

      • Sad to say, I think the reason you did better than the experts was precisely because your simple model did not leave room for including any defensive measures by the community. The professional modellers probably assumed that the leadership at the top could not possibly be as incompetent as it has been. The simple model winds up being right because it did not assume an intelligent response–and that is the right assumption whenever Trump and Kushner are involved…in anything.

  23. @Ecoquant

    Calculated column derived from google spreadsheet:

    #pos/(#pos+#neg) Date
    0.188295160693358 20200404
    0.193221490388134 20200403
    0.188543755492412 20200402
    0.183284635987339 20200401
    0.176144049740174 20200331
    0.169899264859968 20200330
    0.167271104503393 20200329
    0.160708654567598 20200328
    0.158691936865991 20200327
    0.155457524771921 20200326
    0.151656339257755 20200325
    0.150717120378751 20200324
    0.150826734604058 20200323
    0.141469410939816 20200322
    0.129515482451732 20200321
    0.126002367214085 20200320
    0.116216109006525 20200319
    0.104523020755865 20200318
    0.107318994130553 20200317
    0.100166986516462 20200316
    0.123362233194666 20200315
    0.125306873977087 20200314
    0.123720630833602 20200313
    0.140551517742625 20200312
    0.147830970096869 20200311
    0.169683751363141 20200310
    0.147810680840294 20200309

    • @drf5n, Thank you very much. Interesting. Hard to know, but it looks like there was a dilution effect of some kind 20200313-20200319.

      • Yeah. We had some large step-ups in testing capacity around then, and maybe were able to test more than just the sickest folk. My suspicion is that with limited tests, they mostly go to the hospitals with the most cases and they then allocate them to the sickest folks.

        Somewhere out on the wild internet I read that you need to be testing such that you get at least a 15:1 ratio of negatives to positives (<6.25% positve) to get a handle on an outbreak. That might be enough capacity to test and trace a set of contacts, but we've never been close.

        Folks are looking for serology tests to test more widely and get more representative samples so we can make better inferences about the number of infected, susceptible, and recovered folks.

      • 15:1. Sounds about right.
        The UK test rates of positive/total are now running at 48%, up from 35% a week ago. 5th May – 5,903 positives out of 12,334 tests (or ‘tested people’ to be exact). Good old Boris. It’s great when the country is being run by such as he and surrounded by yes-men.

  24. Not sure whether here or the more recent post is the best place to deposit this comment, but the University of Washington is doing purely Bayesian projections of COVID-19 prevalence and forecasting accordingly. They also project hospital utilization and have a resources page. They are funded by the Bill and Melinda Gates Foundation.

  25. My dtr is responding well to the antibiotic and steroids. That was a good combo because the steroids would suppress the deadly so-called “cytokine storm” that sometimes happens with large initial dose. cytoking response is the immune system’s sledge hammer. antibodies are more like a surgical immune response. Imagine your immune system hitting your lungs with a sledge hammer. That situation puts you in ICU with very damaged lung tissue and need for ventilator to stay alive while your immune system tries to catch up. More on cytokine storm here:
    stay well all. mike

  26. There’s too little data to do much with the observations, and it is probably not a major form of transmission, but some work has suggested SARS-CoV-2 might be carried by pollution seeded water droplets long distances. I’m tracking that, and I have not found a lot of good original work.

    This was done looking at spatial correlations with wind patterns which might have carried these from heavily infected regions.

    If there were an Azalel long shot (the normative flip of a “Hail Mary pass”) like that, it could explain a couple of mysteries.

    First, no one understands how the lions and tigers in New York’s zoo came down with COVID-19: None of their keepers tested positive.

    Second, an odd thing about the distribution of active cases in the United State is that apart from city centers where you’d expect concentration, the distributions are amazingly uniform. See the snap from the Johns Hopkins site below. Those could correlate with road networks, but I have not done the study and need to dig up road networks data some place:

    Wind spreading could help explain.