The Corona Virus

[NichG]

In my own mathematical modeling (not an epidemiologist), a psuedo normal distribution works best, which comes out to

new cases daily = e^(C - (days away from the peak)^2). Which is probably optimistic, as these things tend to have a long tail.

A simple exponential model kind of works so far, if you allow for a gradual reduction in rate from social distancing and weird artifacts from testing in early days of the development.

China's official numbers have become really weird, doubly so in comparison to the rest of the world, triply so with rumors of hush money and large urn purchases. Apart from the second and third things, the rate of new deaths versus new cases is 25%. There are delays involved, so a weird ratio of some occasions is to be expected, but the weird pattern has be holding steady during our crisis.

The problem is that if you've got a growth curve, the evidence about the saturation point is (exponentially) weak before you're past the inflection point. So fit uncertainties are really bad for things like when it will inflect (peak), when it will saturate, etc. I'd want to as much as possible transform the data into a frame in which I'm not fitting according to those things, but instead fitting according to the things which are robust over most of the curve (e.g. growth rate).

There's evidently a pretty deep mathematical modelling problem in here. I've been following someone who is trying to do proper MCMC on this kind of model using multiplicative noise (which is more natural for growth processes) rather than additive noise, and basically it doesn't converge unless you can do one of the integrals analytically (because for multiplicative noise, if you tried to fit a Gaussian to it for example you'd find that the second moment doesn't converge even under infinite sampling).

[HandofShadows]

Maybe some good news. (Hopeful look)

COVID-19 Vaccine Candidate Shows Promise

Seems the University of Pittsburgh Medical School and UPMC (a major Hospital network) had been doing research into a vaccines against coronavirus's (SARS and others) and adapted that tech to fight the new one. Still has to go into human trials, but if it works it can be mass produced quickly. (Crosses Fingers)

[Quizatzhaderac]

things which are robust over most of the curve (e.g. growth rate).

I'm not really sure what you mean by that. The US has had it's current growth rate for five days. I plotted it as a simple exponential a on the 20th (averaging the rates over the past six for the future), and I'm delighted to say I was wrong as that naive plot showed cases passing 1,500,000 in the US today.

Or maybe you meant world rates, but those have been going up because of America.

Or if you mean robust over the curve present and future, which would be the worst kind of begging the question. The question being what shape the curve is and the known fact that it's impossible for the curve to be exponential after the peak (and unlikely to be exponential near it).

The problem is that if you've got a growth curve, the evidence about the saturation point is (exponentially) weak before you're past the inflection point.

That is entirely true, and I'm under no illusions that my projections are any good.

[Tyndmyr]

In my own mathematical modeling (not an epidemiologist), a psuedo normal distribution works best, which comes out to

new cases daily = e^(C - (days away from the peak)^2). Which is probably optimistic, as these things tend to have a long tail.

A simple exponential model kind of works so far, if you allow for a gradual reduction in rate from social distancing and weird artifacts from testing in early days of the development.

China's official numbers have become really weird, doubly so in comparison to the rest of the world, triply so with rumors of hush money and large urn purchases. Apart from the second and third things, the rate of new deaths versus new cases is 25%. There are delays involved, so a weird ratio of some occasions is to be expected, but the weird pattern has be holding steady during our crisis.

Yeah. China's numbers are...very suspect. The deaths/cases ratios do not make a lot of sense in many cases, and there are other worrying things. The whole "no new cases at all" for a long time, followed by a resumption of cases seems to be more likely incorrect reporting than the actual truth.

As for the modeling goes...it is indeed still too early to say for certain much of anything. We're still definitely in the earlier part of the graph. It does seem that US cases have at least slightly inflected downward recently, but that is...well, it could be from other factors as well, such as hitting limits of hospital systems to diagnose in certain areas. So, slight note of possible hope with big, big caveats about the data.

[Rockphed]

So I have been keeping track of the aforementioned graph, and their note about when things are final is misleading. Since monday, the number of new cases on the 16th has gone up by about 1000. That said, on a log-plot there is almost a line before that day and it is pretty much flat afterward. I'm not sure if the lock-downs and social distancing are being very effective, and it is possible that the infection has just hit the point where there are only so many new people to infect every day, but I think most of the current growth is caused by testing more people, not by the virus infecting people without bound.

[veti]

Thanks for the link. But boy is that depressing.

It's significantly better than the numbers I was hearing last week. And it projects the whole thing to be over by August, which is better than I would have guessed.

Seems the University of Pittsburgh Medical School and UPMC (a major Hospital network) had been doing research into a vaccines against coronavirus's (SARS and others) and adapted that tech to fight the new one. Still has to go into human trials, but if it works it can be mass produced quickly. (Crosses Fingers)

So long as you're clear, "mass produced quickly" doesn't mean it will be available to anyone before, at the very earliest if they rush everything and cut every possible corner, early next year.

Yeah. China's numbers are...very suspect. The deaths/cases ratios do not make a lot of sense in many cases, and there are other worrying things. The whole "no new cases at all" for a long time, followed by a resumption of cases seems to be more likely incorrect reporting than the actual truth.

I have been assuming for a long time that the reporting is very suspect from - well, basically everywhere. Some places don't test you unless you turn up in hospital with breathing difficulties, which is a pretty high threshold. France had an apparent spike in reported deaths yesterday, because they hadn't been counting people who died in nursing homes - adding them in made for another 800-plus deaths reported on a single day, although in reality they've been happening over weeks. Here in New Zealand, until a few weeks ago you could only get a test if you had both symptoms and "epidemiological reasons", i.e. you'd been in contact with someone who's been abroad recently, which partly explains why it took them so long to detect community transmission - their own testing rules meant they couldn't find it.

Every country has its own rules and procedures, and its own definitions. In the US, to some degree, the same applies to every state. So the figures will never provide an exact apples-to-apples comparison. That doesn't mean they're worthless, but it's not safe to draw conclusions just from them, without taking into account a lot of other information that's not so easy to plot on a graph.

[halfeye]

It's significantly better than the numbers I was hearing last week. And it projects the whole thing to be over by August, which is better than I would have guessed.

The quicker it's over, the more stressed the health services will be. I myself fear it will be over in three months with a lot of people dead.

It's going to be a different world afterwards.

[Iruka]

Yeah. China's numbers are...very suspect. The deaths/cases ratios do not make a lot of sense in many cases, and there are other worrying things. The whole "no new cases at all" for a long time, followed by a resumption of cases seems to be more likely incorrect reporting than the actual truth.

IIRC, they had previously not counted people who tested positive but did not show any symptoms.

It's significantly better than the numbers I was hearing last week. And it projects the whole thing to be over by August, which is better than I would have guessed.

That depends on what you mean by 'over'. The pandemic itself would only truly be over when the majority (I heard 60-70%) of the population has an immunity. If we flatten the curve sufficiently to not overburden our health systems, this would take a really long time. So vaccination is the only other option, which I would expect to still take about a year until we have reached sufficient immunity.
The scenario I have seen for Germany is to keep the current strict measures for about two months, to get the number of infected below ~1000. This is an estimate for the number of people we can reasonably keep track of and isolate. From that point on it is basicallly walking on eggshells with travel restrictions and no mass events until the herd immunity is established.

[Bartmanhomer]

The Coronavirus actually reminds me of the Crush Card Virus in Yu-Gi-Oh. Oh, the humanity.

[Rockphed]

IIRC, they had previously not counted people who tested positive but did not show any symptoms.



That depends on what you mean by 'over'. The pandemic itself would only truly be over when the majority (I heard 60-70%) of the population has an immunity. If we flatten the curve sufficiently to not overburden our health systems, this would take a really long time. So vaccination is the only other option, which I would expect to still take about a year until we have reached sufficient immunity.
The scenario I have seen for Germany is to keep the current strict measures for about two months, to get the number of infected below ~1000. This is an estimate for the number of people we can reasonably keep track of and isolate. From that point on it is basicallly walking on eggshells with travel restrictions and no mass events until the herd immunity is established.

There are 2 ways to end a pandemic: either everyone who can get infected is immune, or all reservoirs of the disease are extinct. Part of why measles keeps coming back is that there are reservoirs of it in primate populations. If we can track down everyone who might have the disease we might be able to quarantine those people and let everyone else go about their lives, and then the pandemic will be over in about a month.

[veti]

That depends on what you mean by 'over'.

If you look at the projection I was responding to, by August there will be no more deaths, no more hospitalisations. That's pretty well "over", in my book. I find it kinda hard to believe, but that's what the graphs show.

[Forum Explorer]

If you look at the projection I was responding to, by August there will be no more deaths, no more hospitalisations. That's pretty well "over", in my book. I find it kinda hard to believe, but that's what the graphs show.

That's surprising and contradictory to the information released about the Corvid-19 infections in Ontario. But really, they are modelling a novel disease that we really don't know too much about. So I don't really believe either projection.

[NichG]

I'm not really sure what you mean by that. The US has had it's current growth rate for five days. I plotted it as a simple exponential a on the 20th (averaging the rates over the past six for the future), and I'm delighted to say I was wrong as that naive plot showed cases passing 1,500,000 in the US today.

Or maybe you meant world rates, but those have been going up because of America.

Or if you mean robust over the curve present and future, which would be the worst kind of begging the question. The question being what shape the curve is and the known fact that it's impossible for the curve to be exponential after the peak (and unlikely to be exponential near it).That is entirely true, and I'm under no illusions that my projections are any good.

Lets say I have a process like:

S -> I at rate max(a+b*eta,0)*I*S where eta is a unit Gaussian
I -> R at rate c*I

This will give an exponential growth phase, a peak, and an exponential decay. The issue is that during the growth phase, I wouldn't expect the statistics of cases on a given day to be Gaussian - rather, it should be log-normal because of the multiplicative noise. E.g. the log of the number of cases on a given day should be Gaussian.

So depending how you do curve fitting to this data or even if you're using something like point estimates to accelerate MCMC, things like estimates of the number of cases or the variance can be really bad. When the model passes into the saturating regime, the statistics of the number of cases becomes Gaussian again.

Since we have data primarily in the growing regime, that makes me not trust things which are parameterized in terms of specific case numbers and times outside of the growing regime, unless that transition in the statistics of the fluctuations is taken into account. On the other hand, I would expect Gaussian estimates of the distribution of possible average growth rates to be generally okay during the growing phase, because that quantity is linear in the log-transformed coordinates - so the multiplicative noise becomes additive noise.

To put it another way, if we collect data day by day, our best estimate of the average growth rate of Covid-19 should converge steadily like 1/sqrt(N), but our best estimate of when the peak will be or how many cases we should expect one week later won't converge in a regular way like that.

Edit: Also, reading the paper from the interactive model, that curve is what you get if you use Wuhan's behavioral response as a model. Weaker responses will be systematically worse than the predictions on that page. So that's the optimistic result.

[factotum]

If we can track down everyone who might have the disease we might be able to quarantine those people and let everyone else go about their lives, and then the pandemic will be over in about a month.

aka the South Korea approach...

[Iruka]

There are 2 ways to end a pandemic: either everyone who can get infected is immune, or all reservoirs of the disease are extinct. Part of why measles keeps coming back is that there are reservoirs of it in primate populations. If we can track down everyone who might have the disease we might be able to quarantine those people and let everyone else go about their lives, and then the pandemic will be over in about a month.

I would assume the perfect identification and quarantine of several hundred thousand people is rather theoretical ...

If you look at the projection I was responding to, by August there will be no more deaths, no more hospitalisations. That's pretty well "over", in my book. I find it kinda hard to believe, but that's what the graphs show.

I did look at it. From their FAQ:

Why do your estimates only go until July? Does that mean the outbreak will be over then?

Our model says that social distancing will likely lead to the end of the first wave of the epidemic by early June. The question of whether there will be a second wave of the epidemic will depend on what we do to avoid reintroducing COVID-19 into the population. By end the of the first wave of the epidemic, an estimated 97% of the population of the United States will still be susceptible to the disease, so avoiding reintroduction of COVID-19 through mass screening, contact tracing, and quarantine will be essential to avoid a second wave.

Those 40k-180k dead would be just the first wave. Of course, we would be not back to square one if the disease would start spreading again since people will be much quicker with counter measures and more testing and protection equipment will be available.

[Eldan]

There are 2 ways to end a pandemic: either everyone who can get infected is immune, or all reservoirs of the disease are extinct. Part of why measles keeps coming back is that there are reservoirs of it in primate populations. If we can track down everyone who might have the disease we might be able to quarantine those people and let everyone else go about their lives, and then the pandemic will be over in about a month.

Eeeexcept that there seem to be studies that show that immunity to the virus may not last longer than a few weeks to months after infection, so it might just keep coming around.

[NichG]

Eeeexcept that there seem to be studies that show that immunity to the virus may not last longer than a few weeks to months after infection, so it might just keep coming around.

The only one I've seen so far suggests that for other viruses in this family, antibody titers decayed over the course of about 5 weeks, but reinfections that did occur after that period were much more mild. Of course the caveat is that this was a related virus, not this particular strain. Not sure if there's any large-scale evidence yet as far as the persistence of immunity for this virus (a couple stories of possible re-infections of people, but no bulk statistics yet that I've seen at least).

Edit:

I spent way too long on this after the discussion with Quizatzhaderac, but here's what I mean about the growth rate vs peak time thing. I made a model that infers the parameters a,b,c from the SIR thing that I posted before given time-series of data. You can then plug these back into the model and simulate a bunch of runs to see when you think the peak will be given the data so far.

The estimate of a and c (growth rate and decay rate) both converge moderately well within the first few data points, though there's some residual (probably due to the way I'm doing the inference) - basically you get within 20% of the value given something like 10 days of data. On the other hand, the peak time is systematically underestimated on the approach to the peak, and just using a Gaussian measure (standard deviation) consistently puts the real peak time at an extreme of the range.

Note also that the estimate for b never converges - this is the noise coefficient, and I think that's related to the point about sampling rare events and how b connects to the statistics.

Here's a link to the plot (can't inline it with Google Drive).

[Strigon]

I would assume the perfect identification and quarantine of several hundred thousand people is rather theoretical ...

That's only necessary to eradicate the disease. To stop the pandemic, we ony need to be "good enough" at identification and quarantine. And the idea of social distancing for the next few months is partially to reduce the number of infected to a more manageable level. Which will all be much easier this time, because we already have experience tracking it, and people aready know how quickly it can turn bad - meaning less resistance to measured taken to contain it. If we happen to find a treatment in the meantime,
You don't have to reduce a disease's growth to zero in order to handle it effectively.

Eeeexcept that there seem to be studies that show that immunity to the virus may not last longer than a few weeks to months after infection, so it might just keep coming around.

Kinda-sorta. First off, that's not really proven, so take it with a grain of salt. Secondly, "immunity" doesn't really exist in a binary form. People say you "can't" get some infections twice, but that's not strictly true - for pretty much every disease, there are people who have contracted it twice, because the immune system isn't perfect. You might have a 10^-8 chance of catching it, but I don't think that it's ever 0. Likewise, if "immunity" only lasts a few weeks, you'll still have some measure of resistance - this wouldn't just reduce the severity of the disease if you do catch it, it woud also reduce your likelihood of catching it. Because even if your "immunity" has worn off, it's still there in some form. Even if those already infected are only 40% less likely to catch it, that still makes a difference. And if the remaining 60% have a shorter sickness (and thus infectious period,) that will also make a difference.

[Kaptin Keen]

So .. Denmark has set a date for partial re-opening. After easter, children will return to school and daycare.

And obviously, this has caused near-infinite uproar, with people shouting (on social media) that the government is experimenting on children. I'm still waiting for the first one to claim it's child murder.

Never mind the fact that children spread the disease much less than adults, are much less prone to have serious complications - and how little difference it makes whether baby Anton or his dad brings covid-19 into the household. Never mind that if dad goes back to work, there's no one to take care of baby Anton.

Me, I'm just waiting to see if there are going to be actual, massed demonstrations in front of parliament. Oh, the irony.

[Iruka]

That's only necessary to eradicate the disease. To stop the pandemic, we ony need to be "good enough" at identification and quarantine. And the idea of social distancing for the next few months is partially to reduce the number of infected to a more manageable level. Which will all be much easier this time, because we already have experience tracking it, and people aready know how quickly it can turn bad - meaning less resistance to measured taken to contain it. If we happen to find a treatment in the meantime,
You don't have to reduce a disease's growth to zero in order to handle it effectively.

The estimates about the number of 'trackable' cases was about 1000 for Germany. So we would still need to wait a while until we reach that.

So .. Denmark has set a date for partial re-opening. After easter, children will return to school and daycare.

And obviously, this has caused near-infinite uproar, with people shouting (on social media) that the government is experimenting on children. I'm still waiting for the first one to claim it's child murder.

Never mind the fact that children spread the disease much less than adults, are much less prone to have serious complications - and how little difference it makes whether baby Anton or his dad brings covid-19 into the household. Never mind that if dad goes back to work, there's no one to take care of baby Anton.

Me, I'm just waiting to see if there are going to be actual, massed demonstrations in front of parliament. Oh, the irony.

I would trust dad more with keeping a distance and being careful about touching stuff than baby Anton. I agree with the problem of a lack of child supervision but that would only apply to a part of the workforce ...

[Kaptin Keen]

I would trust dad more with keeping a distance and being careful about touching stuff than baby Anton. I agree with the problem of a lack of child supervision but that would only apply to a part of the workforce ...

.... not in this country (depending on precisely what you mean).

Yea, kids will be less stable in keeping distance, but on the other hand, they've had a few weeks to learn. And the goal isn't to keep them from getting sick - but to keep what seems to be called the infection pressure low. Apparently, we aim for an infection pressure of 1,25.

[Joran]

So .. Denmark has set a date for partial re-opening. After easter, children will return to school and daycare.

And obviously, this has caused near-infinite uproar, with people shouting (on social media) that the government is experimenting on children. I'm still waiting for the first one to claim it's child murder.

Never mind the fact that children spread the disease much less than adults, are much less prone to have serious complications - and how little difference it makes whether baby Anton or his dad brings covid-19 into the household. Never mind that if dad goes back to work, there's no one to take care of baby Anton.

Me, I'm just waiting to see if there are going to be actual, massed demonstrations in front of parliament. Oh, the irony.

Johns Hopkins (one of the US' premier health care universities) shows children still as a vector of infection; I haven't seen anything that children don't spread the disease as well as adults, just that they have better outcomes and lower mortality.

"Children and intrafamilial spread appear to be a growing means of transmission."

https://www.hopkinsguides.com/hopkin...9__SARS_CoV_2_

The issue is that the children are going to interact with people who aren't children, (childcare workers, parents, grandparents, etc). Even healthier and younger people like Anton's dad has a chance to be seriously ill and die.

"Adults 20–44 account for 20% of hospitalizations, 12% of ICU admissions."

[Wardog]

There is a common meme going around that many/most people who apparently died "from" covid19 actually just died "with" it - i.e. they were about to die anyway from some other "underlying condition" and covid19 just changed the cause.


Well, here is some science dubunking that notion. It's calculated that on average people dying from covid19 are on average dying 11 or 13 years early for women and men respectively.
https://wellcomeopenresearch.org/articles/5-75

[Grey_Wolf_c]

There is a common meme going around that many/most people who apparently died "from" covid19 actually just died "with" it - i.e. they were about to die anyway from some other "underlying condition" and covid19 just changed the cause.


Well, here is some science dubunking that notion. It's calculated that on average people dying from covid19 are on average dying 11 or 13 years early for women and men respectively.
https://wellcomeopenresearch.org/articles/5-75

In the same vein, here is a bunch of graphs showing expected death rates versus actuals, and of the actuals, which have been blamed on COVID. If anything, it shows that we have grossly underestimated the deaths by COVID.

https://www.economist.com/graphic-de...sgraphicdetail

Grey Wolf

[factotum]

Yeah, that "theory" that people are just dying *with* the disease is absolute cobblers, you just have to look at the death rates as they are now compared to last year to realise that--you don't get a statistical increase like that without some underlying cause.

[Chen]

In the same vein, here is a bunch of graphs showing expected death rates versus actuals, and of the actuals, which have been blamed on COVID. If anything, it shows that we have grossly underestimated the deaths by COVID.

https://www.economist.com/graphic-de...sgraphicdetail

Grey Wolf

I guess it depends on how sharply the covid curve comes down (which it probably wont do). Some of those latest year flu curves are pretty crazy. 2017 peak is only a couple thousand deaths below the covid one and I dont remember hearing anything that year.

[Kaptin Keen]

In Denmark, we have fewer deaths overall, compared to earlier years.

There are so few corona deaths - and the social distancing and other initiatives have reduced all infectious disease to the point that fewer people are dying than usual. There were fresh numbers in the news today.

0,3% of those dead are below the age of 60.
57% of those dead are above the age of 80.
We have 370 dead, and including the 'dark figures' we have maybe as much as 200.000 infected.

On an individual level, this disease is not dangerous. At least, no more dangerous than going out into traffic*. On a national level, it's another picture: Because of it's pattern of spread, it can overwhelm a health sector not prepared for it, and cause deaths disproportionate to it's individual danger.

*And this is not some sort of joke: There are more traffic deaths in Denmark these days than corona virus deaths.

And then I just want to point out that saying all this in no way is meant to make light of the problems in countries that have been less fortunate than Denmark.

[Tvtyrant]

I guess it depends on how sharply the covid curve comes down (which it probably wont do). Some of those latest year flu curves are pretty crazy. 2017 peak is only a couple thousand deaths below the covid one and I dont remember hearing anything that year.

It also infected 40,000,000 instead of 700,000, which is a pretty huge difference. If Covid infected 40,000,000 the death toll would be over a million.

[Peelee]

It also infected 40,000,000 instead of 700,000, which is a pretty huge difference. If Covid infected 40,000,000 the death toll would be over a million.

If Covid infected 40,000,000 the death toll would be over a million.

If

I admire your optimism.

[halfeye]

It also infected 40,000,000 instead of 700,000, which is a pretty huge difference. If Covid infected 40,000,000 the death toll would be over a million.

Here they're apparently only counting you as infected if you have to go into hospital, and also apparently they don't count you as recovered at all, so we have infected and deaths, and the uninfected. So it's possible that the number of people who've had the disease is much higher, but nobody knows.