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Modeling coronavirus spread, or why are there different numbers of expected deaths?

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  • Modeling coronavirus spread, or why are there different numbers of expected deaths?

    I've been seeing some confusion about the output of epidemiological models in some recent articles in the general press. It's often presented as "one scientist said a million people are going to die, but now they say only 10,000" or something equally confusing. So i thought it might be helpful to discuss these models, how they work, and how they're being used.

    If you have an epidemic in your country, and you want to know how much it's going to spread, you can make some rough ballpark estimates using things like population size and infectiousness of the pathogen. But things are much, much more complicated than that. People who were infected once tend to be immune and can't spread it further. People won't get infected if they never come in contact with an infected person. Etc. etc. Epidemiological models are meant to take all these complications into account, and give a more realistic picture of what a disease might do.

    So, for example, one model I looked at uses census data to create a per-county population model of the entire US. It then figures out the possibility of spreading an infection based on data on the average classroom size of each school, as well as the office size of companies in each building, etc. For each disease you use it to model, you also put in details like the infectivity and lethality of the disease, how many infected people arrive from other countries, etc. The model can then do daily estimates of how the epidemic progresses.

    Now, for the coronavirus pandemic, we'd obviously want to use data specific to this virus, like its fatality rate and how many people each infected person tends to pass it on to. And here already you run into challenges. Do you take the infectivity rate from South Korea, which kept the virus in check, or Italy, which didn't? Do you use the global average lethality, or assume a lower value because you know that many people with mild symptoms were never tested?

    The exact assumptions used in a model is an area that experts can disagree on. So, two people could use the same model and get somewhat different results, based on their choices in configuring it. This isn't a matter of one number being right and the other wrong - both numbers are right for the set of assumptions used to configure the model. Which set of assumptions is closer to reality can be tough to tell with a fast moving pandemic like this one.

    The other cause of confusion is that somethings you want to model hypotheticals. What happens if a country does nothing in response to the arrival of the virus? (That's a potentially useful "worst case" scenario that can put an upper bounds on the sorts of problems we might see.) What happens if social distancing starts three weeks into an outbreak? What happens if half the population decides not to obey social distancing advice?

    We know that many of these conditions are completely unrealistic. Crowded Spring Break beaches already showed us that lots of people are stupid when it comes to the advice of health experts, so you'll never get full, nation-wide isolation. And we already know that some states started social isolation early out of caution, before the virus had hit them too hard. So, we know in advance that the numbers produced by those model runs are going to be "wrong" in the sense of not reflecting what we'll see in the real world. But it can be useful to planners because it gives a sense of how the outbreak might progress under different control approaches, so that they can identify an approach that might be optimal.

    Just to be clear on that last point: it's sometimes useful to run models that we know are going to be "wrong" in the sense of not reflecting real-world behavior.

    Finally, it's important to note that models run a few weeks ago may rely on data on policies and human behavior that quickly become out of date. So, while they might have been "right" based on what we knew at the time, things changed since then, making them "wrong" in the sense that their results are no longer relevant.

    Hopefully, that gives people a sense of how the same general approach of modeling the epidemic can produce very different numbers. So, if you see headlines like "scientists thought 3 million would die, now they're saying 30,000", chances are that what you're looking at are different model runs that may have very different assumptions baked in. It's not a matter of scientists disagreeing with each other or having no idea what's going on.
    "Any sufficiently advanced stupidity is indistinguishable from trolling."

  • #2
    There is an interesting section in httpgs://ourworldindata.org/coronavirus concerning the problems predicting mortality rate, risk of dying, and the different methods to determine this. In summery the data is not good enough to make an accurate calculation. The problem is the inconsistent testing for coronavirus infection. China's statistics are a mess with
    under reporting the number of deaths. In the USA there is not near enough testing to calculate any mortality rate.South Korea had a comprehensive testing program and indicated a mortality rate of 0.6%.

    Source: https://ourworldindata.org/coronavirus



    There is a straightforward question that most people would like answered. If someone is infected with COVID-19, how likely is that person to die?

    This question is simple, but surprisingly hard to answer. There are several numbers that can help us get towards it – statistics such as the total number of confirmed cases, and the number of deaths so far – but those measures don’t tell us everything we need to know.

    Here we explain why that is, and what we can be sure about. We’ll discuss the “case fatality rate”, the “crude mortality rate”, and the “infection fatality rate”, and why they’re all different.

    The key point is that the “case fatality rate”, the most commonly discussed measure of the risk of dying, is not the true answer to the question, for two reasons. One, it relies on the number of confirmed cases, and many cases are not confirmed; and two, it relies on the total number of deaths, and with COVID-19, some people who are sick and will die soon have not yet died. These two facts mean that it is extremely difficult to make accurate estimates of the true risk of death.

    The case fatality rate (CFR)
    In the media, the risk of death from COVID-19 is usually presented as the “case fatality rate”, sometimes called case fatality risk or case fatality ratio, or CFR.

    But this is not the same as the risk of death for an infected person – even though, unfortunately, journalists often suggest that it is. It is relevant and important, but far from the whole story.

    The CFR is very easy to calculate. You take the number of people who have died, and you divide it by the total number of people diagnosed with the disease. So if 10 people have died, and 100 people have been diagnosed with the disease, the CFR is [10 / 100], or 10%.


    But it’s important to note that it is the ratio between the number of confirmed deaths from the disease and the number of confirmed cases, not total cases. That means that it is not the same as – and, in fast-moving situations like COVID-19, probably not even very close to – the true risk for an infected person.

    Another important metric, which is very different from the CFR, is the crude mortality rate.

    The crude mortality rate
    The “crude mortality rate” is another very simple measure, which like the CFR gives something that sounds like the answer to the question that we asked earlier: if someone is infected, how likely are they to die?

    But, just as with CFR, it is actually very different.

    The crude mortality rate – sometimes called the crude death rate – measures the probability that any individual in the population will die from the disease; not just those who are infected, or are confirmed as being infected. It’s calculated by dividing the number of deaths from the disease by the total population. For instance, if there were 10 deaths in a population of 1,000, the crude mortality rate would be 10/1,000, or 1%, even if only 100 people had been diagnosed with the disease.

    This difference is important: unfortunately, people sometimes confuse case fatality rates with crude death rates. A common example is the Spanish flu pandemic in 1918. One estimate, by Johnson and Mueller (2002), is that that pandemic killed 50 million people.29 That would have been 2.7% of the world population at the time. This means the crude mortality rate was 2.7%.

    But 2.7% is often misreported as the case fatality rate – which is wrong, because not everyone in the world was infected with Spanish flu. If the crude mortality rate really was 2.7%, then the case fatality rate was much higher – it would be the percentage of people who died after being diagnosed with the disease. [We look at the global death count of this pandemic and others here.]

    Before we consider what the CFR tells us about the mortality risk it is helpful to see what the CFR does not tell us.

    What we want to know isn’t the case fatality rate: it’s the infection fatality rate
    Remember the question we asked at the beginning: if someone is infected with COVID-19, how likely is it that they will die? The answer to that question is captured by the infection fatality rate, or IFR.

    The IFR is the number of deaths from a disease divided by the total number of cases. If 10 people die of the disease, and 500 actually have it, then the IFR is 10/500, or 2%.30,31,32,33,34

    To work out the IFR, we need two numbers: the total number of cases and the total number of deaths.

    However, as we explain (here) the total number of cases is not known. That’s partly because not everyone with COVID-19 is tested.35,36

    We may be able to estimate the total number of cases and use it to calculate the IFR – and researchers do this. But the total number of cases is not known, so the IFR cannot be accurately calculated. And despite what some media reports imply, the CFR is not the same as – or, probably, even similar to – the IFR. Next, we’ll discuss why.

    © Copyright Original Source



    Read on for more details.
    Glendower: I can call spirits from the vasty deep.
    Hotspur: Why, so can I, or so can any man;
    But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

    go with the flow the river knows . . .

    Frank

    I do not know, therefore everything is in pencil.

    Comment


    • #3
      Originally posted by shunyadragon View Post
      There is an interesting section in httpgs://ourworldindata.org/coronavirus concerning the problems predicting mortality rate, risk of dying, and the different methods to determine this.
      Source: OWID

      When there are people who have the disease but are not diagnosed, the CFR will overestimate the true risk of death.

      © Copyright Original Source


      I don't think this is true, the question is whether we have a representative sample (of ages, genders, nationalities, etc.). Underreporting deaths, by China (as you mentioned) would skew this number.

      Blessings,
      Lee
      Last edited by lee_merrill; 03-29-2020, 04:38 PM.
      "What I pray of you is, to keep your eye upon Him, for that is everything. Do you say, 'How am I to keep my eye on Him?' I reply, keep your eye off everything else, and you will soon see Him. All depends on the eye of faith being kept on Him. How simple it is!" (J.B. Stoney)

      Comment


      • #4
        Originally posted by lee_merrill View Post
        Source: OWID

        When there are people who have the disease but are not diagnosed, the CFR will overestimate the true risk of death.

        © Copyright Original Source


        I don't think this is true, the question is whether we have a representative sample (of ages, genders, nationalities, etc.). Underreporting deaths, by China (as you mentioned) would skew this number.

        Blessings,
        Lee
        I am not sure what your point is here. Yes, based on the difficulty of determining the numbers of infected people makes the CFR difficult to calculate. The data available estimates that over time the death rate drops, but yes the accuracy is difficult to calculate. The data from South Korea (0.6%) is the best we have, but it is an estimate that is over a period of time. The death rate in Korea is much lower than China by any even rough limit in China in part, because China greatly underreported the casualties. We will have to wait for some long term test data for larger populations to get a better estimate of change over time
        Glendower: I can call spirits from the vasty deep.
        Hotspur: Why, so can I, or so can any man;
        But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

        go with the flow the river knows . . .

        Frank

        I do not know, therefore everything is in pencil.

        Comment


        • #5
          Source: https://time.com/5798168/coronavirus-mortality-rate/

          Looking at data from countries with robust testing systems does support the idea that the disease’s mortality rate may be lower than 3.4%. Countries that have tested significant numbers of people are generally reporting lower mortality rates than those, like the U.S., that have tested in far lower numbers and with a stronger focus on severe cases. This suggests that when testing networks are broadened to catch people with less serious illnesses, and case counts then reflect this range of severity, mortality rates go down.

          The mortality rate in South Korea, where more than 1,100 tests have been administered per million residents, comes out to just 0.6%, for example. In the U.S., where only seven tests have been administered per million residents, the mortality rate is above 5%.

          © Copyright Original Source

          Glendower: I can call spirits from the vasty deep.
          Hotspur: Why, so can I, or so can any man;
          But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

          go with the flow the river knows . . .

          Frank

          I do not know, therefore everything is in pencil.

          Comment


          • #6
            Originally posted by lee_merrill View Post
            Source: OWID

            When there are people who have the disease but are not diagnosed, the CFR will overestimate the true risk of death.

            © Copyright Original Source


            I don't think this is true, the question is whether we have a representative sample (of ages, genders, nationalities, etc.). Underreporting deaths, by China (as you mentioned) would skew this number.

            Blessings,
            Lee
            I realize there are only estimates without firm figures in the number of cases, and particularly in China the deliberate underreporting under reporting of fatalities and cases.
            Nonetheless my one BIG concern now is the outrageous fear based figures put out by Fauci concerning fatality estimates of 100,000 to as much as 240,000.

            If you take the publically released figures of China a densely populated country and triple them you will not come up with any thing close to the outrageous figures that Fauci proposed.
            Glendower: I can call spirits from the vasty deep.
            Hotspur: Why, so can I, or so can any man;
            But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

            go with the flow the river knows . . .

            Frank

            I do not know, therefore everything is in pencil.

            Comment


            • #7
              The pattern of the coronavirus over time is becoming clear when comparing United States, United Kingdom, Spain, and Italy. The comparison shows that Spain, and Italy developed spread of the coronavirus before the USA, and the United Kingdom follow the same pattern. Italy and Spain are beginning to peak into the hump of the bell curve, and the predicted pattern would indicate that the USA and the United Kingdom will follow in a week or so and begin to approach the peak of a natural virus bell curve.

              Look for this graph in this reference:

              Source: https://ourworldindata.org/coronavirus



              OVID-19 – Daily new confirmed deaths – rolling 3-day average

              Limited testing and challenges in the attribution of the cause of death means that the number of confirmed deaths may
              not be an accurate count of the true number of deaths from COVID-19.

              © Copyright Original Source



              I refer to these countries, even though the true number of deaths may not be truly accurate I believe it is reliable for comparison. The case and fatality rates for China are of course, unreliable big time they follow the same bell curve pattern, which is the normal pattern for all the related viruses.

              I predict the total fatalities in the USA to be between 15,000 and at most 30,000. following the natural course of the coronavirus. The total will depend on the success of intervention strategies.
              Last edited by shunyadragon; 04-02-2020, 03:50 PM.
              Glendower: I can call spirits from the vasty deep.
              Hotspur: Why, so can I, or so can any man;
              But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

              go with the flow the river knows . . .

              Frank

              I do not know, therefore everything is in pencil.

              Comment


              • #8
                Originally posted by shunyadragon View Post
                The pattern of the coronavirus over time is becoming clear when comparing United States, United Kingdom, Spain, and Italy. The comparison shows that Spain, and Italy developed spread of the coronavirus before the USA, and the United Kingdom follow the same pattern. Italy and Spain are beginning to peak into the hump of the bell curve, and the predicted pattern would indicate that the USA and the United Kingdom will follow in a week or so and begin to approach the peak of a natural virus bell curve.

                Look for this graph in this reference:

                Source: https://ourworldindata.org/coronavirus



                OVID-19 – Daily new confirmed deaths – rolling 3-day average

                Limited testing and challenges in the attribution of the cause of death means that the number of confirmed deaths may
                not be an accurate count of the true number of deaths from COVID-19.

                © Copyright Original Source



                I refer to these countries, even though the true number of deaths may not be truly accurate I believe it is reliable for comparison. The case and fatality rates for China are of course, unreliable big time they follow the same bell curve pattern, which is the normal pattern for all the related viruses.

                I predict the total fatalities in the USA to be between 15,000 and at most 30,000. following the natural course of the coronavirus. The total will depend on the success of intervention strategies.
                Two things worth noting:

                a) Italy’s Coronavirus Death Toll Is Far Higher Than Reported

                2: There appears to be major differences in different parts of the U.S., like say in California and New York.

                I'm always still in trouble again

                "You're by far the worst poster on TWeb" and "TWeb's biggest liar" --starlight (the guy who says Stalin was a right-winger)
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                Comment


                • #9
                  Originally posted by rogue06 View Post
                  Two things worth noting:

                  a) Italy’s Coronavirus Death Toll Is Far Higher Than Reported

                  2: There appears to be major differences in different parts of the U.S., like say in California and New York.
                  Yeah, the US has a more diffuse population than European countries, so you can't expect a disease that spreads through contact between people to follow the same curve in the two different countries. Also, with the exception of places like South Korea, nobody's built up the testing capacity to start randomly sampling their populations, so we don't know what the real incidence in some of these countries is.
                  "Any sufficiently advanced stupidity is indistinguishable from trolling."

                  Comment


                  • #10
                    Originally posted by TheLurch View Post
                    Yeah, the US has a more diffuse population than European countries, so you can't expect a disease that spreads through contact between people to follow the same curve in the two different countries. Also, with the exception of places like South Korea, nobody's built up the testing capacity to start randomly sampling their populations, so we don't know what the real incidence in some of these countries is.
                    I know you're likely wicked busy right now, but if you get a chance, could you check my math on Imperial College-London Report 9?

                    Comment


                    • #11
                      Originally posted by rogue06 View Post
                      Two things worth noting:

                      a) Italy’s Coronavirus Death Toll Is Far Higher Than Reported

                      2: There appears to be major differences in different parts of the U.S., like say in California and New York.
                      California began its shutdown / social distancing program 2 1/2 weeks before any other state and before the infections got too out of hand. Because of that prompt action the "flatten the curve" strategy seems to be working. The rate of infection growth is much lower than in NY and the peak infection is not projected until early May with a lot lower total. CA is now projected to not run out of hospital beds or ICU room although we're still short about 1200 ventilators. The only downside to "flattening the curve" means the number of infections will decrease slowly too so the "shelter in place" and business shutdown may have to run until June or even later. Still that's a small price to pay for saving 20,000 - 40,000 lives and avoiding the collapse of the hospital system like Italy or Spain.

                      Comment


                      • #12
                        Originally posted by TheLurch View Post
                        Yeah, the US has a more diffuse population than European countries, so you can't expect a disease that spreads through contact between people to follow the same curve in the two different countries. Also, with the exception of places like South Korea, nobody's built up the testing capacity to start randomly sampling their populations, so we don't know what the real incidence in some of these countries is.
                        We don't have real incidence numbers for any country. I doubt that we get it until the serology* is widespread. Which is not to say that we can't use what we have, but incidence is skewed by a number of factors, at least in the short term.



                        *Antibody testing is serological. It is also the only way to gauge inoculation / infection.
                        "He is no fool who gives what he cannot keep to gain that which he cannot lose." - Jim Elliot

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                        Comment


                        • #13
                          Originally posted by Teallaura View Post
                          We don't have real incidence numbers for any country. I doubt that we get it until the serology* is widespread. Which is not to say that we can't use what we have, but incidence is skewed by a number of factors, at least in the short term.



                          *Antibody testing is serological. It is also the only way to gauge inoculation / infection.
                          That's a fair point. I think South Korea was on the ball enough that they seem to have caught most cases as they were happening. But most other countries will probably have people who are post-infection and haven't been tested while the infection was ongoing.
                          "Any sufficiently advanced stupidity is indistinguishable from trolling."

                          Comment


                          • #14
                            Originally posted by Juvenal View Post
                            I know you're likely wicked busy right now, but if you get a chance, could you check my math on Imperial College-London Report 9?
                            I didn't even know there was a health science section here, so that was informative. I'll try to check it out over the weekend.
                            "Any sufficiently advanced stupidity is indistinguishable from trolling."

                            Comment


                            • #15
                              Originally posted by rogue06 View Post
                              Two things worth noting:

                              a) Italy’s Coronavirus Death Toll Is Far Higher Than Reported

                              2: There appears to be major differences in different parts of the U.S., like say in California and New York.
                              The death toll in Italy has complications because of the complicating health conditions and advanced age of the population of most of the victims. Average age of the vitims in Italy was 79.9. It is true that many deaths in Italy were likely reported as other causes.
                              Last edited by shunyadragon; 04-02-2020, 08:58 PM.
                              Glendower: I can call spirits from the vasty deep.
                              Hotspur: Why, so can I, or so can any man;
                              But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:

                              go with the flow the river knows . . .

                              Frank

                              I do not know, therefore everything is in pencil.

                              Comment

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