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Old 04-03-2020, 12:17 PM
The wind of my soul is offline
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Can anyone explain the math to me?


I'm talking to people who are telling me "experts project that the virus will reach its peak at X date," and I keep saying "How do experts know that?"

And basically, that's my question for you guys. To give one example, in my home state of Virginia, I'm looking at this graph showing that in about two months, the number of cases will be going down each day rather than up: https://covid19.healthdata.org/projections. How the hell do they calculate something like that? I mean, I can understand seeing a line on a graph and extending that line out, like if something was increasing exponentially for two weeks, to increase it at that same rate for another two weeks.

What I don't understand is what you can use to project a turning point. Only thing I can think of is if mathematicians took data from elsewhere in the world and tried to fit current data to the same curve, but my understanding is that most countries are still on the uptick.

One thought I had was that maybe they were projecting the point at which so many people were exposed to the disease that it could no longer grow exponentially, but when I read their FAQ page, it said that "By the end of the first wave of the epidemic, an estimated 97% of the population of the United States will still be susceptible to the disease and thus measures to avoid a second wave of the pandemic prior to vaccine availability will be necessary," so that's not it.
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Old 04-03-2020, 12:44 PM
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I think they are estimating the average number of people that one person can infect (based on observation of the increase in infections) - and from that number, you can extrapolate the future number of infections, and when the rate will start to decrease. This video is pretty helpful and shows how changes in the number of people infected by each person affects the curves https://www.youtube.com/watch?v=gxAaO2rsdIs
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Old 04-03-2020, 01:00 PM
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In order to spread the virus needs hosts and if there are lots of other hosts around it can spread easily and continue to infect more and more people. After being infected, the host will either die or recover, but either way, they are no longer a viable host. The virus, as it spreads, is essentially using up all the available hosts. Eventually, the number of available hosts begins to become sparse and the spread slows and, hopefully, stops.

Understanding the transmission rate of the virus dictates how long it will take before the peak spread is reached and eventual decline.

Imagine 1 person in a room with 99 viable hosts. It will spread pretty fast! Now imagine what happens sometime later. Most people in the room have had it, so the the virus has a harder time finding new hosts.
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Old 04-03-2020, 01:33 PM
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Start with this Wikipedia article:
https://en.wikipedia.org/wiki/Mathem...ctious_disease
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Old 04-03-2020, 01:43 PM
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Okay, but did you guys see the last paragraph of the OP? It seems like what you're saying is, essentially, the disease will die down when there aren't as many people to spread the disease to.

If 97% of the population is still susceptible to the disease, then what you're describing doesn't seem to fit the model that healthdata.org is providing. If they were projecting that the number of new cases would start falling in correlation to when new isolation measures were put into place and the disease incubation period had passed, I would understand that.

But to say that they're projecting the curve to start declining on May 24 (for the state of Virginia) doesn't seem to hinge on anything. It's too early for the disease to have reached a critical mass of people, and it's too late for the decline to be a result of any additional isolation measures.
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Old 04-03-2020, 01:51 PM
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Originally Posted by The wind of my soul View Post

But to say that they're projecting the curve to start declining on May 24 (for the state of Virginia) doesn't seem to hinge on anything. It's too early for the disease to have reached a critical mass of people, and it's too late for the decline to be a result of any additional isolation measures.
Yes, to the first part (too early to get to everybody) - but not too late to be the result of isolation. Isolation has a built-in lag - there will be people infected before the isolation started who still turn up sick, and who infect other people who are in isolation and who can still infect the few people they still encounter (family members, etc.), but isolation will gradually start to break the growing chains of infection that would otherwise go on until everyone got sick.

The simulations I mentioned above may help demonstrate that.

Last edited by Andy L; 04-03-2020 at 01:51 PM.
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Old 04-03-2020, 01:58 PM
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Yes, to the first part (too early to get to everybody) - but not too late to be the result of isolation. Isolation has a built-in lag - there will be people infected before the isolation started who still turn up sick, and who infect other people who are in isolation and who can still infect the few people they still encounter (family members, etc.), but isolation will gradually start to break the growing chains of infection that would otherwise go on until everyone got sick.

The simulations I mentioned above may help demonstrate that.
Okay, thanks, that explanation helps. I do intend to watch the video you linked to, but my dog was pestering me to go outside so I haven't yet.
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Old 04-03-2020, 02:10 PM
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Okay, but did you guys see the last paragraph of the OP? It seems like what you're saying is, essentially, the disease will die down when there aren't as many people to spread the disease to.

If 97% of the population is still susceptible to the disease, then what you're describing doesn't seem to fit the model that healthdata.org is providing. If they were projecting that the number of new cases would start falling in correlation to when new isolation measures were put into place and the disease incubation period had passed, I would understand that.

But to say that they're projecting the curve to start declining on May 24 (for the state of Virginia) doesn't seem to hinge on anything. It's too early for the disease to have reached a critical mass of people, and it's too late for the decline to be a result of any additional isolation measures.
Various numbers have been proposed for when we get to "herd immunity", which means basically the density of viable hosts falls to a point where the disease starts to die out. Those numbers are anywhere from 20% to 80%. You don't need 100% of the population to have been infected to have the disease die out. If, for example, you get to 50% that have been infected, it will start to die out.

Looking at the data from that website for Wes Virginia, peak happens on May 4. West Virginia has a population of 1.86Million. I don't know the current hospitalization rate, but I'm going to guess it is below 20%. In China I saw a report it was 15%.

So:
West Virginia population: 1.8 million
Number needed to pass the peak: 900,000
Corresponding hospitalization: 900,000 * 0.2 = 180,000
If you add up the total hospitalizations from that website up to May 4, it is 261,000.
So maybe the authors of that site think the hospitalization rate is higher or they feel a higher percentage is needed for herd immunity.

Either way, May 4 is about right for when we will begin to see herd immunity kick in for West Virginia.
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Old 04-03-2020, 02:16 PM
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Various numbers have been proposed for when we get to "herd immunity", which means basically the density of viable hosts falls to a point where the disease starts to die out. Those numbers are anywhere from 20% to 80%. You don't need 100% of the population to have been infected to have the disease die out. If, for example, you get to 50% that have been infected, it will start to die out.

Looking at the data from that website for Wes Virginia, peak happens on May 4. West Virginia has a population of 1.86Million. I don't know the current hospitalization rate, but I'm going to guess it is below 20%. In China I saw a report it was 15%.

So:
West Virginia population: 1.8 million
Number needed to pass the peak: 900,000
Corresponding hospitalization: 900,000 * 0.2 = 180,000
If you add up the total hospitalizations from that website up to May 4, it is 261,000.
So maybe the authors of that site think the hospitalization rate is higher or they feel a higher percentage is needed for herd immunity.

Either way, May 4 is about right for when we will begin to see herd immunity kick in for West Virginia.
Sorry, ignore this. Screwed up some numbers.
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Old 04-03-2020, 02:22 PM
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...
Imagine 1 person in a room with 99 viable hosts. It will spread pretty fast! Now imagine what happens sometime later. Most people in the room have had it, so the the virus has a harder time finding new hosts.
At this stage of the game, are we sure that being infected with the virus and recovering results in 100% immunity? I seem to recall not long ago that it was uncertain. And what if you are infected just a little (there seem to be gradations), do you get just a little or full immunity?
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Old 04-03-2020, 02:59 PM
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At this stage of the game, are we sure that being infected with the virus and recovering results in 100% immunity? I seem to recall not long ago that it was uncertain. And what if you are infected just a little (there seem to be gradations), do you get just a little or full immunity?
Outside of some very dubious reports of reinfection, I know of no instances of reinfection happening. If you are infected "just a little", I've never heard of the giving you lesser immunity than someone who received a larger viral load, but that is a better question for the experts. I just have never heard of it. The duration of the immunity is not known, but based on the reports I've read it is not expected to be less than a year or two.
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Old 04-03-2020, 04:17 PM
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Various numbers have been proposed for when we get to "herd immunity", which means basically the density of viable hosts falls to a point where the disease starts to die out. Those numbers are anywhere from 20% to 80%. You don't need 100% of the population to have been infected to have the disease die out. If, for example, you get to 50% that have been infected, it will start to die out.

Looking at the data from that website for Wes Virginia, peak happens on May 4. West Virginia has a population of 1.86Million. I don't know the current hospitalization rate, but I'm going to guess it is below 20%. In China I saw a report it was 15%.

So:
West Virginia population: 1.8 million
Number needed to pass the peak: 900,000
Corresponding hospitalization: 900,000 * 0.2 = 180,000
If you add up the total hospitalizations from that website up to May 4, it is 261,000.
So maybe the authors of that site think the hospitalization rate is higher or they feel a higher percentage is needed for herd immunity.

Either way, May 4 is about right for when we will begin to see herd immunity kick in for West Virginia.
I know you said to ignore this because you screwed up some numbers, but regardless of numbers, doesn't this also assume that West Virginia has an alligator filled moat around it?
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Old 04-03-2020, 07:09 PM
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Another way to think of the math is to think of R0, a concept that most by now are well aware of.

R0 is that concept of how many each average infected person will infect. More above 1 the faster it spreads. At 1 it stays stable Below one the transmission slows down. As SARS-CoV-2 first hit a population not practicing any social distancing R0 was thought to be between 2 and 3.

Crowded conditions and lots of mixing of people makes for a higher R0. Having almost everyone around being susceptible to the infection makes for a higher R0. Herd immunity in a particular circumstance is when R0 is effectively less than 1.

Social distancing lowers the effective R0. Having more as not susceptible lowers the effective R0. Between the two, and the nature of the bug, at some point it is effectively under 1.

The various models make assumptions about the bug, some very likely, some that are the best guesses they can pull out of the air. But the basic approach is considering three buckets: Susceptible; Infectious; and Recovered. It gets called the SIR model and Wiki goes over the math of it here. The problem is that the models can only be as sure as we are of the assumptions that go into it.
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Old 04-04-2020, 08:51 AM
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Post-infection immunity probably isn't 100%. I mean, everyone talks about chickenpox working that way, but my sister and I both managed to catch it twice, as kids. But even if post-infection immunity is only 99%, the net effect is nearly the same.

It should also be pointed out that there's now loads and loads of data available for this disease, more than enough to make a fit to even a very complicated model. Everyone keeps saying "But we just don't know". That was true in January, maybe, but it isn't any more.
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Old 04-04-2020, 09:44 AM
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Regarding reinfection/immunity, here's one doctor's opinion, posted March 30 (Jen Gunter, obstetrician and gynecologist):
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Might we see people in close proximity hooking up who both tested positive for Covid-19 and are now 14 days post-positive test? It would not surprise me. However, we donít know much about immunity (protection from reinfection) against Covid-19 after an infection. And because tests are in short supply, many people have presumptive infections but canít be tested.
Source: (NYT paywall)
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Old 04-04-2020, 09:52 AM
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Mathematicians and epidemiologists have been collecting data on pandemics and plagues for centuries. Through exquisite analysis of these data, they have constructed models on how a disease moves through a population. People with big brains have earned doctorate degrees and gone on to extensive post-doctoral studies on this critical topic.

I believe Dr Anthony Fauci is one of these experts. You can see the man's frustration as he is forced to listen to Trump's off the wall projections and assumptions about medication. Fauci works hard to break down the progress of the disease as it spreads through our population, and he has been quietly sounding the alarm for some time: it will get worse before it gets better.

There are no cut-and-dried predictions. Nobody can say, "In two weeks, we'll see the decline in new cases." This is a numbers game, and it works on probability. The slope of the curve created by new cases is the crucial focus now. There will not be a peak, or a hinge point. The curve will begin to level off. Eventually. No one knows when.

The changing shape of this curve right now depends upon the behaviors of the uninfected, and if they can STAY uninfected. Not just for today and tomorrow. We're talking weeks or even months.

And always remember, that area under the curve represents all the sick/dying/dead from this disease.

Sit back. Be patient. Stay home. Wash your hands. Don't be stupid. And continue doing this for weeks, perhaps even months.


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Old 04-04-2020, 09:57 AM
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Post-infection immunity probably isn't 100%. I mean, everyone talks about chickenpox working that way, but my sister and I both managed to catch it twice, as kids. But even if post-infection immunity is only 99%, the net effect is nearly the same.

It should also be pointed out that there's now loads and loads of data available for this disease, more than enough to make a fit to even a very complicated model. Everyone keeps saying "But we just don't know". That was true in January, maybe, but it isn't any more.

The loads and loads of data on this disease are NOT ENOUGH. There needs to be extensive testing for the disease so it can be accurately tracked and asymptomatic carriers identified.

Until then, what we have now is "best guess."

In the hands of an expert like Dr Fauci, I'll take his best guess as an extremely informed best guess. And he has said it will get a lot worse before it gets better.


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Old 04-04-2020, 10:09 AM
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... It should also be pointed out that there's now loads and loads of data available for this disease, more than enough to make a fit to even a very complicated model. Everyone keeps saying "But we just don't know". That was true in January, maybe, but it isn't any more.
Loads of data still is not the key data the models need. "We just don't know" is in fact the true current answer.
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Old 04-04-2020, 11:08 AM
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Until then, what we have now is "best guess."
Yes, that's what a model produces - a prediction based on past data.

One problem I see often is, when scientists/mathematicians produce predictions, there's always a confidence interval (error bar) associated with it. Journalists tend to throw that out and just report the prediction, giving the impression that it's a highly precise prediction.
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Old 04-04-2020, 12:14 PM
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One problem I see often is, when scientists/mathematicians produce predictions, there's always a confidence interval (error bar) associated with it. Journalists tend to throw that out and just report the prediction, giving the impression that it's a highly precise prediction.
Yes, but I'm afraid that, even then, most people aren't going to know what a confidence interval is, and are going to assume that the actual value is guaranteed to be within that interval.
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Old 04-04-2020, 12:25 PM
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The uncertainty goes beyond even the broad confidence intervals because there is no way to know how much confidence to have on some basic assumptions to very broad ranges.
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Old 04-04-2020, 03:11 PM
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I know you said to ignore this because you screwed up some numbers, but regardless of numbers, doesn't this also assume that West Virginia has an alligator filled moat around it?
I'm assuming the models that the OP linked to were using each state as an isolated set. But you'd have to ask the people doing the data crunching by state.

Is there ANY model you know of that is taking into account travel into and out of the area? Projection rates for the UK, US and every other country probably rely on very little perturbation from outside influences.

I don't know what the model is using to determine the peak, but my guess would be transmission rates as more are infected and recover. I just can't see this thing going to near 0 with just social distancing, nor why there would be such a drastic difference between states otherwise.

I screwed up because I summed up the number of cases wrong and assumed the peak would happen at something near 50% immunity.

I'd like to learn if the transmission rate drops as infection/recovery rises and if that would explain the drop in the curves, not just social distancing.
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Old 04-04-2020, 03:18 PM
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The uncertainty goes beyond even the broad confidence intervals because there is no way to know how much confidence to have on some basic assumptions to very broad ranges.
I would go beyond that and say that owing to a lack of testing of a representative sample across the population, we know that the data that is available regarding the number of infected people is a gross underestimate, perhaps by an order of magnitude. And any model based upon strict adherence to isolation guidelines is going to underestimate serious cases of COVID-19 and number of of deaths because many people simply aren't practicing isolation or distancing even in states where there are orders and guidance in place.

This epidemic could be stopped in its tracks inside of a month if all actually non-essential people just self-isolated and stayed in the home, and we deployed accurate antibody testing that was readily available so people would know when they are immunized. Neither of these things is happening, and so the unknowns about how this epidemic will trend and when presentations start leveling off is total guesswork at this point. All we can really do is look at countries that responded with approximately the same degree and speed of isolation measures as the US and qualitatively extrapolate from there. And on that basis, we are looking more like Italy and Spain than South Korea or New Zealand.

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Old 04-04-2020, 05:40 PM
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I would go beyond that and say that owing to a lack of testing of a representative sample across the population, we know that the data that is available regarding the number of infected people is a gross underestimate, perhaps by an order of magnitude.
If you know how many have been tested, what criteria were used to select people to be tested, and how many of those tested positive, you could estimate the true number of infected people. There wouldn't be precise, but it may be reasonably accurate.
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Old 04-04-2020, 06:00 PM
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I have heard that the newest models are having to account for the tendency of people in certain areas to believe in nutty conspiracy theories, that will cause them to behave in ways contrary to what the experts are telling them (eg. if a group believes that 5G networks cause the virus, they will feel they can congregate in groups with no problem).

In the past, models operated under the assumption that most people were intelligent, and would do what medical people told them. Not anymore. Models have to be adjusted accordingly.
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Old 04-04-2020, 06:23 PM
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Okay, thanks, that explanation helps. I do intend to watch the video you linked to, but my dog was pestering me to go outside so I haven't yet.
No problem. Am I right in thinking that your question is about how a model can have a result that shows a peak in infections before all people have been infected (i.e. how a model can have a final total number of infected people that is significantly less than the total population)?

If so, one way to think about the situation is that social isolation creates many many subpopulations that don't interact (or really, interact very rarely compared to how people interact inside each subpopulation) - so while some subpopulations end up with almost everyone getting the disease, other subpopulations never encounter the disease at all (yes, this is a bit of a handwaving explanation, but captures the benefits of social distancing well enough, I think).
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Old 04-04-2020, 07:13 PM
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There hasn't been extensive testing in the US. But there has been in other populations, such as Korea and the Diamond Princess, and the data from that extensive testing can be used to calibrate what we know from the limited testing we've done here.
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Old 04-04-2020, 07:26 PM
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If you know how many have been tested, what criteria were used to select people to be tested, and how many of those tested positive, you could estimate the true number of infected people. There wouldn't be precise, but it may be reasonably accurate.
Well, the big unknown is the number of asymptomatic or marginally symptomatic people who have not (and for the most part, cannot) gotten an antigen test. I did some casual modeling early on with one of the parameters being the number of asymptomatic or presymptomatic with ultimate mild presentation were spreaders. Even assuming half of all infected people were asymptomatic or had symptoms not significant enough to report I got ridiculously high R0 values. When I made only symptomatic infected in a range of 10%-20% infected the R0 values started to become more plausible (although still higher than the estimates coming from authoritative sources based upon the data available at the time, mostly from the Wuhan outbreak) but then I ended up with very high rates of overall infection to get the geographical spread that was being shown at the time.

In retrospect, having talked anecdotally with so many people who had "a little cold" or "a bit of flu" in late January or February, and seeing how much the asymptomatic positive tests rise with more available testing, I'm inclined to believe that the virus has spread very widely and most infected people don't realize that they are carrying and spreading the virus. But I wouldn't even want to hazard a rough guess at the total number of infected people except to say that it is likely at least an order of magnitude greater than testing would indicate. We really need post-infection antibody testing to give a credible estimate at this point because many people who may have been infected have probably cleared the virus from their systems.

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I have heard that the newest models are having to account for the tendency of people in certain areas to believe in nutty conspiracy theories, that will cause them to behave in ways contrary to what the experts are telling them (eg. if a group believes that 5G networks cause the virus, they will feel they can congregate in groups with no problem).

In the past, models operated under the assumption that most people were intelligent, and would do what medical people told them. Not anymore. Models have to be adjusted accordingly.
I don't know how you would even go about trying to build this kind of behavior into a model. I'm sure that there are sociologists working on models of how conspiracies spread and how they affect behaviors but I don't know how you would then tie that into some kind of compartmental model to predict the effect of behavior on infection spread on a local level. I guess you'd have to use some kind of heuristic modeling technique to capture feedbacks, but then information, misinformation, and guidance from government officials has been changing so quickly you wouldn't even be able to have some kind of equilibrium state to compare the model predictions to (mostly non-existent) sample data. There are socio-epidemiological models on how vaccination or the lack of affects infection rates for diseases like the measles but they are post hoc models that look at the effectiveness of vaccination campaigns and public education efforts, not predictive models to trend epidemic outbreaks.

As for the possibility of reinfection, since this is a 'novel' virus we really don't know how much immunity exposure conveys, but for every other infectious virus that the immune system develops a response to having been exposed provides at least significant immune response for at least a few years, and often for the patient's lifetime. However, that response can be inadequate if the patient has a compromised immune system or the virus mutates sufficiently that the T cells no longer recognize the pathogen derived proteins associated with the virus, hence why people can present shingles from the normally dormant varicella zoster (chickenpox) virus when stressed or immunocompromised.

FiveThirtyEight: "Why Itís So Freaking Hard To Make A Good COVID-19 Model":
So, imagine a simple mathematical model to predict coronavirus outcomes. Itís relatively easy to put together ó the sort of thing people on our staff do while buzzed on a socially isolated conference call after work. The number of people who will die is a function of how many people could become infected, how the virus spreads and how many people the virus is capable of killing.

See? Easy. But then you start trying to fill in the blanks. Thatís when you discover that there isnít a single number to plug into Ö anything. Every variable is dependent on a number of choices and knowledge gaps. And if every individual piece of a model is wobbly, then the model is going to have as much trouble standing on its own as a data journalist who has spent too long on a conference call while socially isolated after work.
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Old 04-04-2020, 07:33 PM
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The numbers are only predicting what we KNOW at the the time the numbers are being calculated.

For instance, we knew about the price of gold and what it was likely to do. Then the gold was found in California and the gold rush changed everything rendering that obsolete.

Even places like South Korea, the testing isn't that complete and things like false positives, false negative and lifestyle choices.

Add to that, we in America still are not treating symptoms but rather telling people go home and when you get sick enough go to the hospital. There are a lot of symptoms of pneumonia which can be treated early on. We're not doing, whereas places like Germany are.

Then we have the whole quesiton of asymptomatic carriers. On the Princess Cruise, 20% of passengers that were positive showed no symptoms then and still haven't gotten ill.

Is this a statistical anomaly or does it account for why pockets of people falling ill are seemingly springing up out of nowhere?

Bottom line is garbage in, garbage out. Your results are only good as the numbers going into it. Expect it to change as we get more information.

It's going to be a good five years after this ends, before we get meaningful accurate analysis of what happened.

Last edited by Carryon; 04-04-2020 at 07:33 PM.
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Old 04-04-2020, 07:35 PM
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I think they are grossly underestimating the amount of people infected but not sick enough to seek treatment. Even those who call in sick are told to shelter in place and never are tested or become data. We have no reliable data on the virus to base our decisions on. Mass testing on the general public needs to be carried out.
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Old 04-04-2020, 07:52 PM
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Originally Posted by Chronos View Post
There hasn't been extensive testing in the US. But there has been in other populations, such as Korea and the Diamond Princess, and the data from that extensive testing can be used to calibrate what we know from the limited testing we've done here.
The Diamond Princess is a highly biased population sample: not only is it older, wealthy people from a country where a lot of people have specific chronic underlying health issues due to lifestyle choices (COPD, diabetes, obesity, et cetera), but it is also people who were in close contact with other infected people for a significant length of time. The data from the Diamond Princess might inform a model of how the virus spreads in that specific type of environment (and thus, might be useful for estimating contagion in the case of the USS Roosevelt) but it is really not a good representation of the US or other national populations as a whole.

South Korea is a better sample because they have done widespread testing of basically anyone who wanted to be tested, so they have a lot of data with a presumably broad demographic representation (although I would assume the people who got tested either had some symptoms or was in close contact with someone else who did, so there may still be bias), but the more significant issue is that South Korea took the sort of early steps to limit contagion like distancing and closing down public venues, while the US did not (and in many states still is not) doing these things. So the distribution in a representative sample of South Koreans tells us what the infection rate and R0 looks like in what is essentially the best case response, but it is essentially an unachievable lower bound per capita for what we will see in the United States, or what other countries that were slow to respond like Great Britain will look like.

What is really needed is geographically extensive sample testing of both the 'hot spots' and the places that are not yet hot but are going to be soon (which is basically going to be everywhere in the country), both antigen testing to see who is infected and antibody testing to see who was infected but is now immunized so you can make good estimates of how likely the remaining uninfected to be exposed.

To address the question of the o.p., we'll have a reasonable estimate of when peak deaths will occur once the rate of hospitalizations flattens out, because there is a pretty consistent correlation between hospitalizations with critical symptoms and fatality rates with some compensation for the number of people who will die because they cannot receive critical care for lack of ventilators and medication. When new hospitalizations flatten out, peak deaths will occur 2-3 weeks later because that is about the time it take to either succumb or recover sufficiently to be removed from ICU care. That is really the best answer anyone has that doesn't come with absurdly wide error bars.

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Old 04-05-2020, 09:10 PM
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Originally Posted by Stranger On A Train View Post
FiveThirtyEight: "Why Itís So Freaking Hard To Make A Good COVID-19 Model":
So, imagine a simple mathematical model to predict coronavirus outcomes. Itís relatively easy to put together ó the sort of thing people on our staff do while buzzed on a socially isolated conference call after work. The number of people who will die is a function of how many people could become infected, how the virus spreads and how many people the virus is capable of killing.

See? Easy. But then you start trying to fill in the blanks. Thatís when you discover that there isnít a single number to plug into Ö anything. Every variable is dependent on a number of choices and knowledge gaps. And if every individual piece of a model is wobbly, then the model is going to have as much trouble standing on its own as a data journalist who has spent too long on a conference call while socially isolated after work.
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Would a Monte Carlo analysis be of use in a situation like this?
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Old 04-05-2020, 09:36 PM
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Would a Monte Carlo analysis be of use in a situation like this?
So, I have quite a bit of experience with Monte Carlo methods because this is exactly how you do launch vehicle stability simulations and certain types of sensitivity analysis in reliability engineering. Monte Carlo methods are useful because they allow you to test models that have far more parameters than you could compare with some kind of ANOVA analysis, particularly when you have some kind of time-varying model when the behavior in the future has a strong dependence to previous conditions, and you are testing to see how likely a violation of some stability or reliability threshold is. However, like any simulation or analysis, if you put garbage in you get garbage out. And with epidemiology, the types of models they run tend to be compartmental models that look at aggregated behavior because of the sheer amount of data and difficulty trying to represent individual incidences of transmission, so in general they really aren't interested in trying to predict individual transmissions at a global level. (There are "track and trace" efforts to follow index patients in an outbreak but once a disease is at the epidemic level there are simply too many infections to follow.)

In the case of the SARS-CoV-2 pandemic, there is so little reliable random sample test data that trying to estimate parameters to a model is pure guesswork. The current estimate from the White House that total deaths from COVID-19 will be 100,000 to 240,000 is without apparent basis other than being the low end of the confidence interval for the current best estimates.

Washington Post: "Experts and Trumpís advisers doubt White Houseís 240,000 coronavirus deaths estimate"
At a task force meeting this week, according to two officials with direct knowledge of it, Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, told others there are too many variables at play in the pandemic to make the models reliable: ďIíve looked at all the models. Iíve spent a lot of time on the models. They donít tell you anything. You canít really rely upon models.Ē
From Marc Lipsitch, Harvard T.H. Chan School of Public Health:

Washington Post: "Far more people in the U.S. have the coronavirus than you think. We arenít testing enough to control the outbreak. The real count could be 10 times higher."

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Last edited by Stranger On A Train; 04-05-2020 at 09:41 PM.
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Old 04-05-2020, 10:00 PM
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So, it's hard to model this thing, but we are told over and over again to 'trust the experts' because they spend their whole lives...trying to model things that are hard to model?
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Old 04-05-2020, 10:41 PM
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So, I have quite a bit of experience with Monte Carlo methods because this is exactly how you do launch vehicle stability simulations and certain types of sensitivity analysis in reliability engineering. Monte Carlo methods are useful because they allow you to test models that have far more parameters than you could compare with some kind of ANOVA analysis, particularly when you have some kind of time-varying model when the behavior in the future has a strong dependence to previous conditions, and you are testing to see how likely a violation of some stability or reliability threshold is. However, like any simulation or analysis, if you put garbage in you get garbage out. And with epidemiology, the types of models they run tend to be compartmental models that look at aggregated behavior because of the sheer amount of data and difficulty trying to represent individual incidences of transmission, so in general they really aren't interested in trying to predict individual transmissions at a global level. (There are "track and trace" efforts to follow index patients in an outbreak but once a disease is at the epidemic level there are simply too many infections to follow.)

In the case of the SARS-CoV-2 pandemic, there is so little reliable random sample test data that trying to estimate parameters to a model is pure guesswork. The current estimate from the White House that total deaths from COVID-19 will be 100,000 to 240,000 is without apparent basis other than being the low end of the confidence interval for the current best estimates.

Washington Post: "Experts and Trumpís advisers doubt White Houseís 240,000 coronavirus deaths estimate"
At a task force meeting this week, according to two officials with direct knowledge of it, Anthony S. Fauci, director of the National Institute of Allergy and Infectious Diseases, told others there are too many variables at play in the pandemic to make the models reliable: ďIíve looked at all the models. Iíve spent a lot of time on the models. They donít tell you anything. You canít really rely upon models.Ē
From Marc Lipsitch, Harvard T.H. Chan School of Public Health:

Washington Post: "Far more people in the U.S. have the coronavirus than you think. We arenít testing enough to control the outbreak. The real count could be 10 times higher."

Stranger
I work far more on the failure analysis end of things than the design end. There are overlaps. but my job doesn't usually entail predicting fail rates, although occasionally there is some of that. In other words, I know of Monte Carlo, but nothing in detail. Thanks for the clarification. I always thought of it as a way to take a broad range of variable inputs and look to see how those variations stack up in the output. That seems to fit what his happening here, where things like R0, hospitalization rates, asymptomatic rates, etc. all make it rather difficult to accurately predict outcomes. I realize it will always be garbage in = garbage out, but sometimes the noise can cancel out.

So again, I appreciate the response. I thing I understand a little better.
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Old 04-05-2020, 11:03 PM
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So, it's hard to model this thing, but we are told over and over again to 'trust the experts' because they spend their whole lives...trying to model things that are hard to model?
"The experts" have empirical knowledge about what has worked or not worked in the past, what can be done to try to avert the worst case scenarios and reduce harms, and how to look for trends. No actual expert can make any good predictions or reliable models without quality data, and because of the appalling lack of testing in the US and elsewhere, there is little in the way of data to be had.

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Old 04-05-2020, 11:18 PM
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I'm assuming the models that the OP linked to were using each state as an isolated set. But you'd have to ask the people doing the data crunching by state.

Is there ANY model you know of that is taking into account travel into and out of the area? Projection rates for the UK, US and every other country probably rely on very little perturbation from outside influences.

I don't know what the model is using to determine the peak, but my guess would be transmission rates as more are infected and recover. I just can't see this thing going to near 0 with just social distancing, nor why there would be such a drastic difference between states otherwise.

I screwed up because I summed up the number of cases wrong and assumed the peak would happen at something near 50% immunity.

I'd like to learn if the transmission rate drops as infection/recovery rises and if that would explain the drop in the curves, not just social distancing.
I understand, but U.S. states are far different than nation-states. There are no border controls and people are free to come and go as they please. I just don't know how you make a state by state model when people from hot spot areas like NY can just go to their hunting cabins in WV or WY and carry the virus with them unknowingly.
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Old 04-06-2020, 10:27 AM
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I understand, but U.S. states are far different than nation-states. There are no border controls and people are free to come and go as they please. I just don't know how you make a state by state model when people from hot spot areas like NY can just go to their hunting cabins in WV or WY and carry the virus with them unknowingly.
I would think there is a bigger problem with border cities. Kansas City is a really good example. NYC and the NYC area border 2 other states.
Yes, there is a lot of fluidity between states, but what else are you going to do? I really don't know how they model these things, so anything I proffered would be a guess, at best. In the end, I still think the inter-state/inter-country mixing is going to be small compared to what is already in state, in addition to the it likely averaging out to be a net zero (people going into NY might roughly match the people coming out, for example.)
  #39  
Old 04-06-2020, 11:49 AM
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Here are two anecdotes to give an idea of how loosey goosey all this is.

1. My good friend in Berkeley Ca, working in an international field at Cal, came down with "something" on March 12, immediately self-isolated, did not get tested (she would not have qualified for a test anywhere in the USA that I know of). She did not have a fever but had a terrible dry cough, lost her sense of smell and taste for several days, felt awful for a week. By that point UC had been closed down and she along with everyone else in Berkeley was stuck in her flat anyway. She is someone who will not show up on anyone's data.

2. My sister-in-law in San Jose Ca, a public school aide, came down with "something" in mid March. Fever, cough. Though it was the flu. They had guests in their house, one of whom went home to Massachusetts, ill with the same thing. No test. Nothing.

Since I have a pretty small circle of family and friends, I would extrapolate to say this must be happening everywhere. People are getting somewhat sick and getting over it but no one is tracking it at all. This contributes not just to the spread -- hey I LIVE in Massachusetts, thanks a pile! -- but also to the flattening of the curve, as they are now, presumably, on the other side of it. Correct?
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Old 04-06-2020, 01:25 PM
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No problem. Am I right in thinking that your question is about how a model can have a result that shows a peak in infections before all people have been infected (i.e. how a model can have a final total number of infected people that is significantly less than the total population)?

If so, one way to think about the situation is that social isolation creates many many subpopulations that don't interact (or really, interact very rarely compared to how people interact inside each subpopulation) - so while some subpopulations end up with almost everyone getting the disease, other subpopulations never encounter the disease at all (yes, this is a bit of a handwaving explanation, but captures the benefits of social distancing well enough, I think).
Yes, that's basically my question. I did watch the video you posted on Friday evening, and it was helpful. Your comment brings up another intriguing thought experiment, which is how the conclusion of social distancing laws will be determined. If the idea is to restrict the disease to small subpopulations, then we may be seeing social distancing laws in place well after the disease has appeared to peak and recede. And indeed, that site I linked to in the OP mentioned that the projections assumed social distancing through August.
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Old 04-06-2020, 02:17 PM
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I think they are grossly underestimating the amount of people infected but not sick enough to seek treatment. Even those who call in sick are told to shelter in place and never are tested or become data. We have no reliable data on the virus to base our decisions on. Mass testing on the general public needs to be carried out.
Or at the very least, we need to use the data from somewhere else that does that.

I mean, it seems to me like the horse has left the barn on universal testing*, but if we used say...the data from Iceland, we might get a better inkling of how things might turn out.

*for multiple reasons, not least of which is that we don't have an antibody test to identify mild cases that have come and gone already. So if someone got it in say... February, and they've recovered from their minimal symptoms, current testing would lump them in the "haven't had it" category, which is about as misleading as not testing as all.

Ultimately all they're trying to do with the modeling is take current guestimates about R0 and population density, hospital numbers, degree of lockdown, etc... and mathematically model how the disease would spread. It's not exact, but it's better than licking a finger and sticking it up to see which way the wind is blowing.

For example, statewide, the models I've seen predict an early-May peak for Texas, but the local officials are talking like it's going to hit about a week or so earlier than that for DFW- in the next couple of weeks. So the model isn't exactly accurate for my specific area, but for the state as a whole, it might be.
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Old 04-06-2020, 08:42 PM
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The nice thing about mathematics is that there are many different ways to arrive at the wrong answer. If all the individual things are both unknown and quite variable, no model will produce a number with great confidence.

One approach is to look at information from various countries - case numbers over time, or better, patients needing hospitalization, ICU or dying. Ignoring important data like testing rates, social structure, medical competence, whether data is honestly reported or useless propaganda, degree of interaction - or trying to match some or all of these - you could come up with a ďmoving averageĒ based on the experiences of other places and assigning weights to the number of cases last week and the weeks before.

You could use a historical approach, looking at (less fatal) outbreaks of similar infectivity, how long they lasted, and then extrapolating.

With better data, you could estimate how many people a person of each age group might infect, the chance of needing hospital/ICU/dying, the reduction from better physical distancing, the effect of reinfection, etc.

The wiki site discusses other forms of modelling, such as SIR and its variants.

Not sure there is great reason to assume it is the same R0 for children and the elderly. In any case, all of the variables are fuzzy and a good article at 538.com explains this effect.

Various simulations can also turn fuzzy data into useless predictions. Whatever model you use, relying on it heavily wonít change whatever really happens.
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Old 04-06-2020, 08:55 PM
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A good explanation.

https://fivethirtyeight.com/features...e-meaningless/
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Old 04-06-2020, 09:04 PM
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And whatever you use, the experts disagree by quite a lot.

https://fivethirtyeight.com/features...ery-far-apart/
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Old 04-06-2020, 09:38 PM
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I think there may be an underlying truth that comes out of the modelling attempts. That is that it seems that not only are the models poorly conditioned, but there may be a real case that reality is itself poorly conditioned, and that the actual flow of the epidemic is very sensitive to the existing conditions. This makes things all that much harder.
OTHO, the curves across the planet all seem to be reasonably well behaved. Despite the variables in testing and diagnosis. It may be that some reporting is deliberately being fudged, but I can't imagine that it is a general pattern. There will be PhDs written for years on this.
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Old 04-06-2020, 10:28 PM
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... Since I have a pretty small circle of family and friends, I would extrapolate to say this must be happening everywhere. People are getting somewhat sick and getting over it but no one is tracking it at all. This contributes not just to the spread -- hey I LIVE in Massachusetts, thanks a pile! -- but also to the flattening of the curve, as they are now, presumably, on the other side of it. Correct?
Yes. https://jamanetwork.com/journals/jam...rticle/2764137

The unusual third hump of this last influenza season countrywide was not likely influenza.

So yes there are likely some significant uncounted numbers who have had infections and contribute to slowing it down as well as to its spread.
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Old 04-07-2020, 03:57 AM
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Various simulations can also turn fuzzy data into useless predictions. Whatever model you use, relying on it heavily won’t change whatever really happens.
Absolutely. I've irritated several friends by pointing this out. They say that the experts say it'll be over in such-and-such weeks, and I rip them apart asking what the experts' assumptions were, talking about the theory of forecasting and how the model is only as good as the data input into it, explaining how experts at analyzing the present are no expert at predicting future events, etc. This irritates them because they really just want to believe it'll be over soon and not think about the reality of the situation that much.

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Thanks, I saw this article and even shared it on Facebook! No doubt the friends I irritated previously didn't take a glance at this article, but a few others did, and it's nice to know some people out there don't want to bury their heads in the sand.

P.S. Just checked the forecast for Virginia again, and the peak resource date jumped from May 24 to April 20. How's that for a volatile model?

Last edited by The wind of my soul; 04-07-2020 at 03:59 AM.
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Old 04-07-2020, 05:44 AM
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Yes. https://jamanetwork.com/journals/jam...rticle/2764137

The unusual third hump of this last influenza season countrywide was not likely influenza.

So yes there are likely some significant uncounted numbers who have had infections and contribute to slowing it down as well as to its spread.
Eh, that’s a pretty big leap to make, from some pretty recent sampling. Going back a little further, Stanford retested a bunch of San Francisco flu and pneumonia patients from January and February, and out of almost 2900 found only two cases, both of them later in February.

https://jamanetwork.com/journals/jam...rticle/2764364

Last edited by Maserschmidt; 04-07-2020 at 05:46 AM.
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Old 04-07-2020, 06:16 AM
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So, it's hard to model this thing, but we are told over and over again to 'trust the experts' because they spend their whole lives...trying to model things that are hard to model?
Hopefully, experts in a field like this will have a much stronger idea about the strengths and weaknesses of various models, will be able to identify bias in their data, and will be able to formulate plans for continuing research in order to narrow the gaps in our understanding. They will understand much better than most people how to calculate, analyze and communicate uncertainty.

Most people don't know anything about statistics. They don't understand sampling bias, confidence intervals, anything like that. Experts in a field will understand how those concepts apply to their research and will have a better understanding, critically, of what they don't know yet.

Experts aren't necessarily right, but they're less likely to be wrong.
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Old 04-07-2020, 06:36 AM
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During January and February test positive influenza was common. Test positive influenza dropped off dramatically end of February. The weird national hump of influenza-like illness (ILI) began end of February.

Yes in January and most of February those who had an ILI (a fairly large number as influenza peaked during January and early February) most likely had influenza on testing. By early March that was no longer the case, most ILI was no longer testing as influenza positive, but an unusual third hump of ILI started up.

That study is not inconsistent with there having been very significant numbers of uncounted cases of infections with SARS-CoV-2.
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