Exponential growth and logarithmic graphs

This is a good explanation of how to spot bullshit graphs in all the horrible news stories you're reading, and how to interpret them properly.

Minute Physics:

It's particularly egregious that so many news reports are comparing number of reported cases in countries whose populations differ by an order of magnitude.

Interactive graph is here.

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46 Responses:

  1. CTD says:

    The only valuable part is the caveats section. Plotting confirmed cases is terrible because there have been so few tests. Only number of deaths is semi-reliable, and in more authoritarian countries, not even that.

  2. tfb says:

    The really disturbing thing is that people are assuming that China have beaten it. They haven't: they've suppressed it by doing enough to get the reproduction rate below 1. If & when they stop doing that it will come back, unless there's a vaccine. So they have to keep doing what they're doing, until then.

    • margaret says:

      this whole exercise is not about beating the virus, it's about not overwhelming hospitals, and cats and dogs living together.

      see the previously and realize we are currently at the "0%" immunity point on the graph, regardless of the borders you call home.

      • NT says:

        Are you the same margaret who confidently asserted last month that masks don't protect the wearer?

        • Kyzer says:

          Regardless of who they are, they were completely correct.

          a beard is about as effective at stopping a virus as a surgical mask is. keep the beard, ditch the mask. a better infographic would be about how and how often one should wash their hands or helpful hints on when to stay at home.

          Wearing surgical masks in public is part of the culture in countries like China, Korea and Japan... and it's completely useless against this virus. What's working is quarantine, isolation, social distancing and hand washing (and contact tracing, etc.)

          Correctly-fitted N95 respirators (not surgical masks) do have some effectiveness, but only people who NEED them should have one right now, healthcare workers and the infected:

          If you are NOT sick: You do not need to wear a facemask unless you are caring for someone who is sick (and they are not able to wear a facemask). Facemasks may be in short supply and they should be saved for caregivers.

          • NT says:

            There is an important difference between "there aren't enough facemasks for medical workers" (true) and "facemasks don't protect the wearer" (a sick lie). Obviously facemasks protect the wearer, that's why medical workers need them.
            Trump's CDC has been pushing disinformation since January. Read the WHO guidelines instead, which explicitly call for a surgical mask for most medical workers (due to shortages) but an N95 if you are performing an aerosolizing procedure. The reports from American ICUs are that even N95 is insufficient, and you really need something like a PAPR if you can get one.

            • Kyzer says:

              Let's be clear:

              1. a surgical mask is pretty much useless for protecting its wearer. Its purpose in medicine is to stop the wearer's phlegm, sputum, etc. ending up in an open patient. Its purpose in popular culture is as a fashion accessory for people with a cold/flu. It socially indicates "I am sick".

              2. an N95 respirator is modestly effective, we agree it's more effective in conjunction with other PPE, and has to be put on carefully (e.g. use disposable gloves every time to put it on and take it off). It should be used indoors where there's a risk of close contact with the infected, not in public as a social status indicator. The way to socially indicate "I am sick" is to STAY THE FUCK IN YOUR FUCKING HOUSE and tell people via social media.

              3. "facemask" is an unhelpfully ambiguous word. Surgical masks are not in short supply at the moment, N95 respirators are.

              Regardless of politics, WHO give the same advice as CDC: "If you are healthy, you only need to wear a mask if you are taking care of a person with suspected 2019-nCoV infection."

              Irregardless of politics, Bruce Aylward conveniently didn't hear your question, so the WHO is politically neutral. (Please don't ignore the advice of medical experts because of geopolitical soap opera)

              • NT says:

                "a surgical mask is pretty much useless for protecting its wearer."
                False. You are deep in Dunning-Krueger territory and this is not a topic to be spreading disinformation about.

                • Anonymouscowardsayswhat?

                • margaret says:

                  this is what you are building your case on? reading comprehension much?

                  While wearing a mask may not necessarily prevent healthy people from getting sick, and it certainly doesn’t replace important measures such as hand-washing or social distancing, it may be better than nothing, Dr. Atmar said.

                  There is very little data showing that flat surgical masks, in particular, have a protective effect for the general public. Masks work by stopping infected droplets spewing from the wearer’s nose or mouth, rather than stopping the acquisition of virus from others.

                  • NT says:

                    That must be the point at which you stopped reading and started posting.
                    Did you read what it said about the flu? (smaller than SARS2)
                    Did you read what it said about SARS1? (similar to SARS2)

                    Do you understand the difference between absence of evidence and evidence of absence?

                  • margaret says:

                    how about we get to the part where you call me a nazi so we can end this thread in a civilized manner?

                  • Leonardo Herrera says:

                    From that same article:

                    When researchers conducted systematic review of a variety of interventions used during the SARS outbreak in 2003, they found that washing hands more than 10 times daily was 55 percent effective in stopping virus transmission, while wearing a mask was actually more effective — at about 68 percent.

              • Dave says:

                1. a surgical mask is pretty much useless for protecting its wearer. Its purpose in medicine is to stop the wearer's phlegm, sputum, etc. ending up in an open patient. Its purpose in popular culture is as a fashion accessory for people with a cold/flu. It socially indicates "I am sick".

                This social attitude is why I've started wearing a bandana (don't have a mask handy) in public. Like Jeffrey Posanker says even a facial cover that doesn't protect me offers at least some protection others, just in case I have COVID-19. I'd also specifically like to destigmatize the wearing of facial coverings for everyone else.

                In my extremely limited experience in southern California the percentage of fellow shoppers with facial coverings has gone up a lot over the last couple of weeks, from two or three at the Costco to about 25% coverage. Since you've informed us surgical masks are not in short supply, we should all work together to push that to 100% for a few weeks and see what happens.

                • jboy says:

                  +1 to Dave

                  In these carefree days of Covid-19, I wear a surgical mask (never an N95 mask or anything needed by our medical professionals) if I must go into a moderately-crowded public area (especially indoors), where I can't guarantee that I can keep 2m from everyone else at all times.

                  Examples include when I go to the supermarket to buy essentials, because unfortunately our supermarkets have shutdown their home-delivery service because it was overwhelmed by demand. (Yes, I know. Way to fix the symptom rather than the problem, guys.)

                  I think of wearing a surgical mask in public as a social courtesy, analogous to coughing/sneezing into my sleeved inner-elbow. Just as coating my inner-arm sleeve with my own mucous & mouth-droplets is unlikely to protect me personally from whatever ails us this week, so too is wearing a mask unlikely to protect me from asymptomatic transmission of Covid-19, but is intended to protect everyone else.

                  It pleases me to know that I'm doing my part to break the chain of contagion (in addition to frequent thorough hand-washing with soap; use of hand-sanitizer; don't touch crosswalk buttons; etc etc yes yes yes).

                  And just as we encourage everyone to cover their mouth & nose when they cough/sneeze, so too do I think we should all be wearing cheap, disposable surgical masks if we must go into crowded public areas.

          • You don't know whether you have the virus or not. That's what's so insidious about this one, there is lots of asymptomatic transmission. Wearing a surgical mask helps stop that. It does nothing to stop the virus from getting in, but it does catch a lot of exhaled droplets. It's not to help you, it's to help others. I expect within a week wearing a surgical mask in public will be the norm here too.

            • NT says:

              "It does nothing to stop the virus from getting in"

              This is a lie being spread for two reasons:
              (1) to preserve masks for others (a good reason but it's still a lie)
              (2) because widespread use of masks is scary and will create panic (a bad reason)

            • NT says:

              This should be common sense. The mask fabric is not directional, if it filters one way it filters both ways. If it's going to leak it will be in the positive pressure direction, i.e. exhaling.

              • jboy says:

                For anyone interested in facts: Actually, the mask fabric is directional.

                Here is an article published by the Hong Kong Centre for Health Protection: https://www.chp.gov.hk/files/pdf/use_mask_properly.pdf

                (I'm sure we can all agree that Hong Kongers take their mask-wearing seriously? Especially after their 17% fatality rate from SARS in 2003?)

                To quote the article:

                Most surgical masks adopt a three-layer design (Annex I) which includes an outer fluid-repelling layer, a middle layer serves as a barrier to germs, and an inner moisture-absorbing layer. Mask without the above functions is not recommended as it cannot provide adequate protection against infectious diseases transmitted by respiratory droplets. Wearer should follow the manufacturers’ recommendations when using surgical mask, including proper storage and procedures of putting on surgical mask (e.g. determine which side of the mask is facing outwards). In general, the coloured side/the side with folds facing downwards of the surgical mask should face outwards with the metallic strip uppermost (Image 1).

                • NT says:

                  Thank you for actually doing the research, I appreciate it. America has a lot to learn from HK, CN, SK, and SG.
                  I think you are reinforcing my point that the purpose of the surgical mask is to protect the wearer though. The important layer for this virus is the middle one, which I still don't believe is directional. The outer layer is for wearer protection from squirts that can occur in surgery but not likely in public.
                  The important thing is to shut down the culture of mask-shaming so that people have social permission to take care of themselves.

            • jboy says:

              +1 to Jef Poskanzer

              Wearing a surgical mask is about protecting everyone else.

              It's crazy that people are (correctly) pointing out that "surgical masks do not protect the wearer" (from aerosols, for example, since surgical masks are not airtight), while completely ignoring (or refusing to acknowledge) the important characteristic of Covid-19 that infected people can be contagious (by droplets) without showing symptoms.

              If everyone wore a mask, it would be like herd-protection.

              Look at two of the countries that have been most successful at holding back Covid-19, which are also two of the countries closest to China: Hong Kong & Taiwan. Both of them have a culture of ubiquitous mask-wearing during flu pandemics. (Both of them were hit hard by SARS in 2003, with fatality rates of 17% & 21% respectively.)

              Here is an article from early March about government-mandated mask production in Taiwan.

              Here is an article from mid March about Taiwan's success at holding back Covid-19.

          • margaret says:

            yes i am and i stand by my statement. an N95 properly fitted, properly worn, properly removed, properly destroyed, ..., is not close to what the general public is capable of doing and has nothing to do with what's caused the cases to go down in china.

            i helped my SO go through a semester of classes were the primary outcome of the class was how to gown-up and down and stay sterile. some people did not pass that class because they couldn't figure out the proper technique needed to protect themselves and others. health care professionals (in california) have to be re-certified and re-fit annually. some random dick-wad walking through costco with a mask is not helping him/herself but is taking resources from others. others who are exposed daily to the coronavirus and who are trying to keep people alive with limited resources.

            currently four floors of my SO's hospital have been turned into highly-contagious "wards" filled with infected patients. as people come and go from these areas their gowns/masks are being removed and resterilized on the spot for the next person to use. what can go wrong?

            even those that are trained and passed certifications can be as stupid or ignorant as the random dick-wad on the street. for example, male hospital workers are refusing to shave their beards/scruff saying the hospital has to supply them with even more expensive and hard to come-by masks.

            further, the mask culture in parts asia isn't about getting sick, it's about keeping your sickness from spreading to others (and in other areas to try to filter pollution out). any little dim flickering of your synapses telling you that the masks, and not draconian lockdown measures, had anything to do with slowing the spread of the coronavirus in china is nonsense.

            • NT says:

              You have no idea what you're talking about.

              "any little dim flickering of your synapses"

              You are not nearly as smart as you think you are. Stop spreading disinformation please.

              • margaret says:

                somewhere you got a load of crap for information and bought it hook line and sinker. you are making shit up to prove your conspiracy theories. good luck with that.

                • NT says:

                  Bitch, I have COVID-19. Because I didn't put my mask on. Because of mask-shaming assholes like you.
                  I gave myself a buzz-cut, shaved, wore a beanie over my hair, wraparound safety glasses and gloves, kept my jaw clenched. But I didn't put the mask on because I knew some shithead would give me flack for wearing it and I thought that the store was probably still safe on 3/15. Wrong.
                  You can discount me for pseudonymity but Jamie knows who I am.
                  Now go fuck yourself. Everybody should be wearing masks except you.

            • rozzin says:

              While the surgical-/manufacturing-/foodservice-style masks do little to prevent the wearer from inhaling airborne particles, they do seem to create a nontrivial barrier to keep people's fingers out of their noses and mouths. And a simple device that enforces "don't pick your nose, lick your fingers, bite your nails...", whether it does so by creating a physical barrier or a psychological one, can do wonders.

              • margaret says:

                i'm happy to agree with this and that they'd help limit the spray of infectious goo. just like my full-face motorcycle helmet does during allergy season.

                so do these laws come off the books? previously.

          • Glaurung says:

            An ordinary facemask protects you by reminding you to not touch your face when you are out and about and are touching surfaces that may be contaminated.

      • tfb says:

        I know that. But I think a lot of people believe that if/when you manage to do what China has done then you're finished & life can return to normal. And since China did it in three months everyone else will do it on about that timescale. And that is not true, and those people are going to get a nasty shock.

        • margaret says:

          i started to question exactly that when they closed disneyland. it'll be interesting to see when and how its deemed safe to open back up. currently there is no end-date.

    • tobias says:

      The most disturbing thing I have seen recently is people assuming that everyone has already caught it in China, South Korea and Japan and people in those countries are therefore immune. Typically these people go on to say 'only flu, get back to work', too.

      • thielges says:

        This is a little like operating a nuclear reactor. China and South Korea basically scrammed the reactor and shut down the chain reaction. They overshot but that was the right thing to do when you have no idea of what the constants are in the reaction equations. Better screech to a halt than risk a meltdown.

        Now they are slowly retracting the control rods by incrementally allowing more out of isolation. That will cause more to get sick though if they are careful the volume of incoming patients will remain manageable.

        Assuming that a vaccine is a year away, this slow burn towards herd immunity might be the most practical strategy.

        • tfb says:

          I think it is the best strategy. The problem is that the time-constants make it very hard. If you do x which makes life better but may increase R too far then the incubation period means you don't know for a week or more whether the thing is running away again, and it can run away quite far in that time. So each x has to be tiny. Exponential processes combined with long control lags are horrible.

          The inverse thing is true currently: the UK has been doing things which (they think) should suppress it for nearly a week but deaths were still increasing at a rate compatible with an exponential yesterday (I haven't checked whether today's numbers still are).

          • Nick Lamb says:

            Unavoidably actual lockdown reduces R0. I can't get infected with this virus by reading about it, or seeing video of people coughing, but I can if I go to spaces where other people are or recently were. Eliminate that and R0 plummets. The problem, for the UK and to a far greater extent the US is that actually locking down and "please try" aren't the same thing and the virus doesn't need to argue with you about whether you were "sincerely trying" not to get it, it'll just cut to the chase.

            One of the ways you can immediately tell the difference is the reaction on TV. If they didn't do it already the Onion should write it - something like journalists reporting on optimistic estimates that no-one will die in blaze at their offices. "Smoke here is getting pretty thick, and I know you'll be struggling to hear me over these alarms but sources are sure that reporters on the upper floors can still respond to the fire and escape before they burn to death if they leave now. Are we live? Let's go again, I feel like I coughed from the smoke and some words weren't clear".

            TV reporters didn't go "Wait, our rolling live news channel isn't essential, what the hell am I doing?" and go home when the announcements were made, and politicians knew better than to point it out. After all, if you're the one politician to point out that these people are ignoring your own advice by being here you won't get coverage and the others will...

            Don't hang on day-by-day numbers. You want to see a prolonged trend - three or four days, preferably a week, to discern anything from the noise, and so together with the lag between infection and diagnosis you won't know if a change in behavior was effective for maybe 10-14 days. If you add a day or two for policy to become behaviour (a hilarious-if-it-weren't-tragic number of Britons reacted to the forced pub closure by immediately going to the pub as if somehow the virus will give them one last chance) you're talking at least two weeks and getting into three from "Announce policy X" to "Find out if policy X was a good idea".

            That's anathema to rolling news. Ideally a story arc lasts no longer than two segments, so you can have a cliff hanger over the commercial break. You can't keep viewers waiting for resolution for three weeks, they'll get distracted, in ten minutes they need to talk to Tom Nook and check Twitter again.

            • tfb says:

              I think you missed what I was trying to say. Obviously you can get R (I am confused about whether R_0 is a constant depending only on the virus and R is the effective thing, or whether R_0 is itself a thing you can tweak with behavioural changes: it does not matter here) very low with suitable behavioural changes ('lockdown'). The problem I'm interested in is when you try/need to relax those changes before there is a vaccine: then the latency between making the adjustment and knowing what its results are severely limits the rate & size of adjustments you can make. My comment about the observed delay after lockdown was just meant to point out that this latency affects changes in either direction, not to imply that I think lockdown does not work.

              I suspect that ruthless testing including testing asymptomatic people, can make the latency better: if you can spot new infections much earlier you can reduce the latency, I would think.

              • Nick Lamb says:

                My understanding was the important thing about R0 is that it assumes a naive population. That is, R0 doesn't vary if you've got a vaccine or if (let's hope) getting the disease once confers immunity for some considerable period even though R would shrink - but R0 would vary based on population behavior. But I am not an epidemiologist so that could be entirely wrong.

                Yes, "pulse" approaches (where you loosen rules then later tighten them again to partly control the infection) will rely on guesswork because of the lag you described, and if they're in use over any substantial period they'll probably also get captured politically rather than run by technocrats, which isn't great.

                Test everybody, trace the infected, isolate all infected by force if necessary would be effective, but it's expensive in every sense. It would have been effective in the US a month ago (and cheaper then than now) but it was too expensive for politicians to stomach. It remains to be seen if it'll be cheap enough (in all the terms politicians care about) to get done in Western Democracies before they lose millions of people.

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