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    • I'm trying to make sense of the fire hose of information we're all currently subjected to, and I thought I might share with you.

      First, there's a dashboard of publicly available information by the German Robert-Koch-Institut (RKI) here:

      That dashboard has a chart for "daily new cases" in the lower right corner, but the numbers there seem to fluctuate wildly based on the fact that some reports from local authorities won't go through on weekends. This means that the number of cases is underreported on the weekend, and in consequence overreported on Mondays and perhaps Tuesdays.

      To make sense of this, I copied the number of new cases into a spreadsheet and plotted that data. X-axis is the number of days since last report of zero new cases on February 25, Y-axis is the number of new cases for that day. The blue line matches the original chart, and the light blue exponential trendline shows a very mediocre fit, as would be expected.

      I then averaged the number of new cases over the last seven days, which should help to get rid of most artifacts based on weekend misreporting. This is the red line - and in fact, the light red trendline is an eerily close match.

      The fact that the end of the red line drops well below the trendline seems promising at first, especially with the 2-person limit in public space enacted the day before - but we need to keep in mind that this is a 7-day average with data lagging behind another day or two since last week, because the RKI switched the way it's getting data on March 16. If this is a real effect and not just a random outlier, this decrease in daily new cases must be based on something that happened perhaps some days ago, perhaps between March 16 and March 20.

      Wikipedia has a detailed timeline of what's going on in Germany, I will have to check this more thoroughly before I have a guess:

    • Are you referring to the dramatically lower reported death rates in Germany versus most of the rest of the world?

      This image at the bottom of this post is a screen grab of the death rates in ten countries around the world,from the NY Times link above, showing number of cases ( I assume this means positive tests not clinical disease but.....), and the number of deaths reported to due to Covid 19..

      I have been struck by this table, which is updated several times a day, for a couple of weeks now, because the German death rates seems to be orders of magnitude smaller than those of Italy, France, Iran, the UK, or the USA. I don't know if this is just due to time differences in reporting or what, but Germany's reported death rates is dramatically lower and has been all along. - not just smaller, but an order of magnitude smaller or more,

      Germany 114 deaths / 27436 cases = .004155 -> ~0.42%

      Spain 2696 deaths / 39673 cases = .06795 -> ~6.8 %

      USA 537 deaths / 43499 cases = .01234 -> ~ 1.2 %

      France 860 deaths / 19856 cases = .04331 -> ~4.3 %

      UK 335 deaths / 6650 cases = .0503 -> ~5.0 %

      China 3277 deaths / 81171 cases = .04037 -> ~4.0 %

      Iran 1812 deaths / 23049 cases = .078615 -> ~7.8 %

      Switzerland 86 deaths / 8836 cases = .009732 -> ~0.97 %

      Italy 6077 deaths / 63927 cases = .09506 -> ~9.5 %

      From this table, Germany's death rate is ~ 1/20th that of Italy - Now is that because of delays in reporting deaths in Germany, or because Italy didn't accurately tally all of its cases, or what. I find it doubtful that German doctors are really that much more capable than those of the UK, or Italy, or Spain. Not sure about their health care systems however.

      So far the US just trails Germany and Switzerland, but that may change a lot in the next couple weeks.

      But a variance in death rates this large begs for an explanation I think...

    • It makes me feel better about myself to be in the distinguished company of Factotum and Pathfiner wrt struggling to understand the data. This chart, however, made me feel a little better after staring at it for awhile:

      You have to grok that it’s a log scale vertically, and also that how far a country’s curve extends to the right is how long since the first death. I believe 3 things. Am I wrong?

      1. Deaths occur 14-21 days after infection, so they lag case numbers. In a place like Italy, since they’ve been doing it longer than Germany, the deaths have had more time to accumulate. That’s why we haven’t seen too many deaths in America yet; most patients haven’t entered their third week.

      2. Incubation takes 2-14 days, so it’s really hard to see cause and effect in Factotum’s graph. Markel gives a speech but do we see any results for 6 days?

      3. Early detection. I watched Netflix’s series Pandemic and the experts were all saying the biggest problem is getting people to come in early when they have the flu. They put it off until it’s serious and harder to save them. China and Korea made testing their mantra and caught cases early and quickly acted. Italy got overwhelmed, fell way behind, and the death rate soared as critical patients flooded their hospitals. We’re doing same in the U.S., which is why I suspect WHO is predicting we’ll be the next epicenter.

    • SO if Germany's death rate is 1/20th that of Italy, are they just 6-12 days behind Italy then?

      If the doubling time is ~ 2 days? Is that the only reason for the disparity in German death rates? Or are there more things to consider?

      At the rate New York is progressing, I can understand the panic. The governor of New York wants all the spare ventilators in the entire country.....

      I mentioned earlier the death rate in Indiana doubled today, from 6-> 12. But as you said, all of those folks fell ill about two - three weeks ago.

    • Are you referring to the dramatically lower reported death rates in Germany versus most of the rest of the world?

      Not specifically, although that is an interesting question as well. I'm mostly interested in understanding the numbers as they come in, because just listening to others interpreting the numbers in various (sometimes mutually exclusive) ways makes me even more anxious than I already am. I'm concentrating on the numbers for Germany because that's where I live and would be most affected by any misrepresentation of the facts, whether done voluntarily or involuntarily.

      In the case of the RKI numbers I linked to above, there is a pattern in the data that shouldn't really be there if it was just tracking an exponential spread. As I mentioned, I expect this pattern (with drops below the trendline each weekend) to be an artifact of the way the ground truth is collected, aggregated and sent up the chain with some inevitable delays.

      This, in itself, is not really dangerous - after all, that's what trendlines and error bars were made for. It potentially becomes dangerous when the media picks up on those numbers exactly on a Sunday, and claims that one of those artificial drops might in fact be a sign that there's potentially a decrease in virus spread itself.

      It's also dangerous if the same media - after having picked up numbers they don't quite understand - now publishes articles attacking the RKI for publishing outdated data, potentially leading to less trust in a institution that currently needs to be trusted. Those are news items I woke up to today...

      The dashboard now contains a disclaimer about data being added to previous days as it arrives (orange part of the bars in the lower right corner). As you can see, there's really not any significant change in the date 5 or more days ago - however, the huge changes in recent data of the last 3-5 days suggest that any drop in the curve we might see towards its end might still be an artifact itself.

    • From this table, Germany's death rate is ~ 1/20th that of Italy - Now is that because of delays in reporting deaths in Germany, or because Italy didn't accurately tally all of its cases, or what. I find it doubtful that German doctors are really that much more capable than those of the UK, or Italy, or Spain. Not sure about their health care systems however.

      So far the US just trails Germany and Switzerland, but that may change a lot in the next couple weeks.

      But a variance in death rates this large begs for an explanation I think..

      I've seen a number of ideas being discussed why this might be the case. I don't know if any or all of them are true, but they at least sound sensible, and might all contribute a little:

      1. Italy's population has a higher average age than Germany's - and additionally, different generations apparently live closer together than in Germany. More elders being infected more easily might mean more severe cases quickly, and thus more deaths.

      2. Italy apparently has mandatory post-mortems including checking for diseases, while this is not always the case in Germany. Some deaths across Germany's elder population might have gone unnoticed.

      3. On the other hand, Germany seems to test more in general. A higher number of virus tests across the general population could reveal more mild cases of the infection, and thus a smaller death rate across all known to be affected.

      4. Better-equipped health system that is overwhelmed less easily, and thus leading to less cases of having to triage and give up some patients... so far.

      5. Last but not least, perhaps the fact that Germany wasn't the first country to be affected led to a slightly better response?

      In the end, Germany lagging behind Italy for some days could explain some of the difference in death rate between the countries, but I don't think it's the only reason. If you compare Germany to France in your chart, for example, you can see that those two countries are on approximately the same "schedule" - but even there, Germany looks to be better off.

    • I wonder if this chart isn't hiding the most important fact in all of its details. What the chart mostly does is track the absolute number of deaths over time. This number isn't completely comparable between countries, though, if you consider that the US has four times the number of citizens than Germany, or thirty times as many as Belgium.

      Also, by aligning all countries on their date of 25th death, it might look as if countries "below the average", the big blob of lines in the lower left, are better off. This must not be the case though, if testing has been sporadic in the beginning and is only becoming more strict now.

      The thing with exponential curves is that nothing really matters as much as the rate of increase. Just as a simple example, consider one country "A" that starts with just one infection, but with cases doubling every day - and another country "B" starting with 1,000 examples and cases doubling every other day.

      Even though country "B" starts with a lot more cases, country "A" manages to catch up with "B" by day 20, and will have two times as many cases just two days later.

      So, the single most important fact of the chart is the incline of each country's trendline when hovering over it (also encoded in each line's color). Considering that, we're currently all in this together, in the "2-3 day doubling" zone.

    • That is why I have been so puzzled by the order of magnitude difference ( ~ ) in death rates between Germany and the rest of the world. I don't know when the infections really first began in the West nor does anyone really. Another one to two weeks should begin to answer a lot of questions, and possibly raise many more.

      I appreciate your thoughtful answer above, but remain less than totally convinced that the five variables you listed are sufficient to explain the dramatic differences. A difference in death rates due to a difference due to post mortem studies is a pertinent fact that I was unaware of. The Italian extended familes have been mentioned and their larger geriatric population with the expected increased risks..

    • That is why I have been so puzzled by the order of magnitude difference ( ~ ) in death rates between Germany and the rest of the world. I don't know when the infections really first began in the West nor does anyone really. Another one to two weeks should begin to answer a lot of questions, and possibly raise many more.

      Can this really be "just a time-shift", though? The difference between Germany and the rest of the world is not in absolute cases, or in rate of growth over time - it seems to be one of severity (or, mathematically speaking, in the ratio of death/affected). I don't see how fast-forwarding alone would change this situation. Even assuming that we fast-forward to a hypothetical point in time where Germany's health system is completely overwhelmed, doing the same for other countries while keeping all other things equal would likely increase their ratio as well, so that a gap would still exist.

    • Hah!!!

      I am not alone in asking about this issue - There is a long article in the Washington Post I saw on Apple News just now -( I have not been a subscriber so I wasn't allowed to grab the link to post here - I know @Chris is is a subscriber, so he may have already seen it. I am looking about on the web as we speak...)

      @Chris will be proud of me, I am now a Washington Post subscriber ) here is the link below - interesting discussion along the lines we discussed @Factotum with more information about the much more aggressive search for positive individuals and isolation of them.

      I have just learned that a nephew of my wife was in Vietnam for a mountain bike race in January, and within a week or two of returning to the US, he, his wife, my sister in law and her husband all had a febrile illness lasting about 5-9 days. None have been tested, but all are convinced they have had Covid 19. They all live in western Pennsylvania. Which helps confirm a thesis that Corona virus has been in the US since mid-January.

      I mentioned earlier that the Governor of Indiana has had estimates that approximately 1% of Hoosiers have been converted ( ~ 67,000) , despite only about 479 + tests and 14 deaths so far.

      I say again, we live in interesting times.

      Here is a description of what the illness is really like to a healthy hearty 50 year old

    • Here's an updated graph, with the following caveats:

      1. Although first information for yesterday, March 25, has been made available via the dashboard, it is clear that the number of cases yesterday is very unreliable data due to reporting delays. For example, yesterday we saw a report of 1,400 cases for the day before (March 24), which has been corrected by 2,200, more than doubling the number of cases, today. Numbers seem to become reliable after that, so I just left out the last day of reporting, which means that this graph contains data up to March 24.

      2. I switched to a log scale on the vertical axis, because that is the best way to plot data that is expected to be exponentially increasing (thanks @Chris for pointing that out via the NY Times chart!). Basically, what that means is that we'd expect a relatively straight line while the number of cases grows exponentially, and any clockwise rotation of the curve (and potentially continuation afterwards on a less steep straight line, without curving up again) is a good thing.

      3. I removed labels for clarity. As pointed out by you guys, any change in the curve necessarily lags behind potential behavioral changes that led to it by at least a week, if not more (incubation + detection + reporting delays), so that it doesn't make sense to add random labels at this point.

    • A question to all mathematicians and data scientists out there:

      Let's suppose that one or another change in behaviour (let's say on day N) does have a significant, positive effect on the virus spread and as such on the number of new cases per day. This means that we're basically looking at two different exponential curves:

      1. on days t=0..N, the curve would best be modeled by exponential function f_1(t) = a*i_1^t

      2. From day t=N forward, the curve would best be modeled by a different exponential function f_2(t) = b*i_2^t + c, with i_2 < i_1, and b and c chosen such that f_1(N)=f_2(N).

      If we're looking at the graph's exponential trendline, we would expect this trendline to closely match f_1 at first, and then eventually closely match f_2 once t has become sufficiently large for the first few values to not matter that much anymore (t>>N).

      The problem obviously is that we're looking at about 2-3 weeks worth of data before any potential change (N~14..21), so that we'd need to have access to several more weeks of data (t>3*N?) before we can have a look at this in hindsight.

      Is there any accepted method to deal with this?

      My gut feeling is that, if we have a curve for days t=0..n and look at its trendline's R², but then also look at the two curves for days t=0..N and t=N+1..n and their trendlines' R², and find a value for N that maximizes the latter two R² values in some form or another, we might achieve something - but I'm not sure how to answer the question of significance. Any ideas?

    • That was a fascinating story in the Post about Germany!

      Epidemiologist Karl Lauterbach, a member of the German parliament, noted that the German outbreak started with large numbers of young people — “people who came back from holidays.”

      The young have fared better with the coronavirus than the elderly. Italy’s initial outbreak struck at the heart of an aging population. Lauterbach said he expected Germany’s death rate to rise as more vulnerable segments of society are infected.

      Because testing is not universal, and many people with the coronavirus might never be diagnosed, a true death rate is impossible to ascertain. But experts say the rate is likely to be significantly higher in countries such as Spain and Italy, where care is collapsing.

      The post is so worth the subscription price...

      I still don’t get why the US has low death rates though. We suck at testing and early outbreaks seemed to occur in the elderly in rest homes or on cruise ships.

    • I've been observing the US individual states rates of infection, on the NY Times map, and Indiana currently reports 479 cases and is currently 19th on that list of Covid cases. We've had 14 deaths so far, and that hasn't been reported as changed since yesterday!

      Higher than I initally expected, as we're not on the coast nor a foreign tourist destination like the coasts. And a bit more rural than urban in many areas.

      BUT Indiana is the 17th largest state in population size, and I am beginning to wonder if the states aren't going to continue to demonstrate a pretty consistent relation in new positives to state populations - in other words, the virus truly is everywhere in the US.... No place to hide.

      Which is what the virologists were all saying 6-8 weeks ago.

      Stay safe my friend! Keep the air in your house moist, take some Vit D ( some marginal evidence it might help ), wash your hands, yada yada yada

      And I agree, the Washington Post was worth the subscription price ! 😄

    • Today's stats for Ontario:

      Population: 13,600,000 (aprx).

      Tests: 38550

      Test results received so far: 27858 (with 10965 pending, 4-5 day lag between test and results)

      Confirmed Cases: 837

      Deceased: 13

      Resolved: 8

      They are not testing those with mild symptoms or those not reporting for testing, so the number of cases is certainly higher. And obviously people with no symptoms are not being tested, either.

      What strikes me is that 97% of the people that are ill enough to be tested are getting negative results! So only 3% of very sick people have Covid-19, and an unknown number of mildly or un-sick people have it.

      Death rate among confirmed cases is 1.5%. Death rate among all people who have test results is 0.03%.

    • Your post kind of confirms my post above - Ontario's population is about twice the size of Indiana's 6.7 million, and 479 cases, Your death count is still similar to Indiana's, but that may change in a day or two.

      I suspect neither Ontario, nor Indiana, are testing anyone who is not symptomatic or possible exposed health care workers. IE: Not attempting to test most of the state/provinces populations.

      Edit - the numbers in the NYT Corona map were just updated when I looked at 2:47 EDT Mar 26

      Indiana now has 645 cases and 17 deaths.

    • If you've seen an earlier reply to your post - I had to delete that, because I misinterpreted the chart you added. I think the following is correct, I got it from the data I already had by:

      - summing up daily new cases for a total up to that point
      - calculating (total_today / total_yesterday)-1 and interpreting that as a percentage
      - averaging over seven of those values for a weekly average

    • To add to the "Italy vs. Germany" mystery, I recently read a comment by an Italian health official, claiming that they are counting those who "died and had the coronavirus", not necessarily just those that died because of it.

      Back-of-the-envelope calculation: I found a 2016 statistic for various causes of death in Italy, according to which something like 850 people per 100K died in that year. Italy has a population of around 60M, which means that about ~500K of them die each year, or ~42K per month.

      If only a small percentage of those people also were being tested positive on SARS-CoV-2 at the time of their death, this might lead to an overcounting of COVID-19-related deaths in Italy in the thousands.

    • Here's the Ontario data today (just 3 days later than the last time I shared? I though that was a week ago!)

      Today's stats for Ontario:

      Population: 13,6 mil. (aprx).

      Tests: 49186 (up from 38550)

      Test results received so far: 41,983 (with 7203 pending, 4-5 day lag between test and results)

      Confirmed Cases: 1326 (up from 837)

      Deceased: 21 (up from 13)

      Resolved: 8 (no change)

      The percentage change in daily new cases since March 17 has remained roughly flat (i.e. flat growth, not exponential growth.

      A graph can be found here (which I can't link to or cut and paste):

      And the Ontario data is here:

      How are you guys doing?

    • I had to go bad and check the date on my posts to be certain.

      On March 26 Indiana reported 645 cases and 17 deaths. Three days later Indiana is reporting 1514 cases, and 32 deaths in the early afternoon. I suspect they will go up significantly before the night is over. Even as reported, at mid-day, cases almost tripled in three days, and deaths doubled in three days.

      At this current rate, in three more days we may have close to 5000 known positive cases and almost 70 deaths

      So with 1/2 the population of Ontario, we have passed you in cases found, and in deaths in just three short days. Way to go Hoosiers!

      I would not say this is not looking good for us, Hoosiers.

      I am staying at home away from people as much as I possibly can.

      @Chris just posted in the main Covid thread, that Fauci is estimating 100,000 to 200,000 deaths in the US this years due to Covid 19......

      CDC reported the death rate for influenza for the winter of 2019/2020 to be between 24.000 and 62,000 for comparision.

      We lose about 34,000 annually due to motor vehicle accidents for comparison.

      I am going to post this link again here - I think it may be that important.

    • How reliable to you feel the data is??

      I have some serious doubts about numbers from a number of countries, and Iran might be one of those countries. Another would be North Korea.

      But then they may do better than the USA, because their citizens do not have the freedoms we do - freedoms that may kill a lot of us, if we aren't careful