Finally a voice of reason

Please.... I've heard that 65568 times!
2^16 = 65536

Definition...
In mathematics, a power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent.
 
Do you have a cite? Because this isn't what I've been hearing anecdotally from friends in the medical community. I should say that I have read the Chinese article in Lancet, but have heard nothing official about the trials taking place in NY. Is that where your info is coming from?

No, I am not aware of a trial in NY (which is not to say there aren't any, I just haven't seen them published). Always happy to provide good citations when possible.

Here is a recent one out of China - http://subject.med.wanfangdata.com.cn/UpLoad/Files/202003/43f8625d4dc74e42bbcf24795de1c77c.pdf
Here is an older one out of China for the related drug Chloroquine phosphate - https://www.jstage.jst.go.jp/article/bst/14/1/14_2020.01047/_article
Here is a study out of France which had fair controls but a small sample size - https://drive.google.com/file/d/186Bel9RqfsmEx55FDum4xY_IlWSHnGbj/view
And here is that Lancet article - https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30132-8/fulltext, which is really not a clinical trial but suggestions for possibly useful drugs.

To somewhat keep up on these, I search each day on scholar.google.com for 'covid-19 treatment' and restrict results to 2020. Most of interesting results in the first 3 pages. I know that a lot of physicians have apparently been prescribing hydroxyquinolone, apparently so much so as to cause a temporary shortage of it at pharmacies.

If people are interested in following this more, I post an update every day or two on my MeWe page which includes any trends in total cases in the US as well as possible treatments being developed. You can add me as a contact if already on MeWe or join and add me. mewe.com/i/petersteinmetz
 
There is the common usage of the word "exponential", and the mathematical one. Pretty sure the one we have been hearing refers to definition 1.

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Pretty sure the one that we have been hearing refers to definition 2. This disease is growing at a rate that mathematically fits an exponential curve. And really, definition 1 is just using words to describe the curve seen in definition 2.


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Pretty sure the one that we have been hearing refers to definition 2. This disease is growing at a rate that mathematically fits an exponential curve. And really, definition 1 is just using words to describe the curve seen in definition 2.


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Some confusion these days may stem from another common current usage. That is when people say one number is exponentially larger than another, with no implication of a change in time or with respect to an independent variable.

That one is a pet peeve of mine and just wrong in my opinion.
 
Pretty sure the one that we have been hearing refers to definition 2. This disease is growing at a rate that mathematically fits an exponential curve. And really, definition 1 is just using words to describe the curve seen in definition 2.
My point is that people use the word "exponential" in common language without regard to the actual math behind the word. "Increase becoming more and more rapid" isn't a math formula.
 
Some confusion these days may stem from another common current usage. That is when people say one number is exponentially larger than another, with no implication of a change in time or with respect to an independent variable.

That one is a pet peeve of mine and just wrong in my opinion.

I completely agree with you. How can one number be exponentially larger than another? No way. Two discrete numbers can be compared by ratio or difference, but they can’t be compared exponentially.


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So I had a few extra minutes so I grabbed the world death data from this site:

https://www.worldometers.info/coronavirus/coronavirus-death-toll/

Plotted it and ran a "best fit" curve.

It looks like the data fits pretty well to the generic exponential equations of f(x)=ae^(kx) in the form of:

f(x)=130.05e^(0.0805x)

Here's the graph. Looks exponential to me.

This data starts on 1/23 and runs through 3/28.
upload_2020-3-29_20-1-2.png
 
My point is that people use the word "exponential" in common language without regard to the actual math behind the word. "Increase becoming more and more rapid" isn't a math formula.

You may be right regarding people’s use of the word in common language, but I assert that increasing becoming more rapid is a perfect description of the behavior of an exponential curve, and that when the news is using it, they are quoting the scientists and doctors who are well aware of the math and know that the spread of a disease in an epidemic can be well modeled with an eponential function.

Using base 2 as an example, and restricting the x values to integers, the binary exponential series is:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...

Seems to me that sequence fits both the definitions well. Mathematically, it’s

f(x) = 2^x

And it’s also increasing at a more rapid rate.

The scary thing is that if x represents some period of time, and f(x) represents the number of people who are infected (or perhaps die from) the Covid 19 virus, then we do have a serious problem...



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You may be right regarding people’s use of the word in common language, but I assert that increasing becoming more rapid is a perfect description of the behavior of an exponential curve, and that when the news is using it, they are quoting the scientists and doctors who are well aware of the math and know that the spread of a disease in an epidemic can be well modeled with an eponential function.

Using base 2 as an example, and restricting the x values to integers, the binary exponential series is:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...

Seems to me that sequence fits both the definitions well. Mathematically, it’s

f(x) = 2^x

And it’s also increasing at a more rapid rate.

The scary thing is that if x represents some period of time, and f(x) represents the number of people who are infected (or perhaps die from) the Covid 19 virus, then we do have a serious problem...
But these models depend on knowing how many cases there are, and testing isn't consistent across regions or even day to day. If some location hasn't been testing many people, then starts testing more, it will skew the curve and make it look like cases are increasing faster than they are. Of course it will also mean there were more cases to begin with. Garbage in, garbage out. It seems that the only way we can gauge the seriousness of the outbreak is to look at the increase in deaths due to COVID-19, or hospital admissions of people testing positive. Anecdotally, it seems that hospitals in some regions of the country and world are becoming overwhelmed. I don't think that happens during the normal flu season.
 
So I had a few extra minutes so I grabbed the world death data from this site:

https://www.worldometers.info/coronavirus/coronavirus-death-toll/

Plotted it and ran a "best fit" curve.

It looks like the data fits pretty well to the generic exponential equations of f(x)=ae^(kx) in the form of:

f(x)=130.05e^(0.0805x)

Sure, but it cannot continue like that. Even though it's a relatively slow growing exponent, in about 9 months, that curve kills everyone on the planet and we know that won't happen. Growing at the same rate, it kills 1% in 6 months, but it will have slowed down long before that. Every curve is going to flatten eventually because the virus will run out of weak members of the herd that succumb to it. This isn't the way to analyze it, it just leads to panic.
 
Sure, but it cannot continue like that. Even though it's a relatively slow growing exponent, in about 9 months, that curve kills everyone on the planet and we know that won't happen. Growing at the same rate, it kills 1% in 6 months, but it will have slowed down long before that. Every curve is going to flatten eventually because the virus will run out of weak members of the herd that succumb to it. This isn't the way to analyze it, it just leads to panic.
You assume the virus does not mutate and then take the stronger members. Or people who have been previously weekend.

Reminder there is no evidence that once sick and recovered you are immune. Further complicating this mentality is there are two strains now in the "wild". As such you need to assume everyone will get it at least twice...
Further there is growing evidence the virus attacks your cardiac system also. So how many will be weekend by the first round...

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Reminder there is no evidence that once sick and recovered you are immune. Further complicating this mentality is there are two strains now in the "wild". As such you need to assume everyone will get it at least twice...

You dont have to assume that. There is no evidence that genetically different strains are sufficiently different immunologically to not have cross-immunity.
 
You're right. I'm also assuming it doesn't morph into a super killer virus with a 100% mortality rate. You also assume the virus does not mutate and become impotent, providing immunity without making anyone sick.

Neither one of the scenarios has anything to do with the current analysis which is sensationalist, unsustainable, and incomplete.
 
anecdotal info......Laura Ingram, of Fox, had a NY subburb doc on a night or two ago and was talking about his success with hydroxyquinoline with azithromycin and zinc. He clams no deaths and starts them on the regiment prior to going on the vent and sees most not need the vent.....and had no deaths....and has treated hundreds.
https://www.foxnews.com/transcript/...-study-on-hydroxychloroquine-and-azithromycin
No, I am not aware of a trial in NY (which is not to say there aren't any, I just haven't seen them published). Always happy to provide good citations when possible.

Here is a recent one out of China - http://subject.med.wanfangdata.com.cn/UpLoad/Files/202003/43f8625d4dc74e42bbcf24795de1c77c.pdf
Here is an older one out of China for the related drug Chloroquine phosphate - https://www.jstage.jst.go.jp/article/bst/14/1/14_2020.01047/_article
Here is a study out of France which had fair controls but a small sample size - https://drive.google.com/file/d/186Bel9RqfsmEx55FDum4xY_IlWSHnGbj/view
And here is that Lancet article - https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30132-8/fulltext, which is really not a clinical trial but suggestions for possibly useful drugs.

To somewhat keep up on these, I search each day on scholar.google.com for 'covid-19 treatment' and restrict results to 2020. Most of interesting results in the first 3 pages. I know that a lot of physicians have apparently been prescribing hydroxyquinolone, apparently so much so as to cause a temporary shortage of it at pharmacies.

If people are interested in following this more, I post an update every day or two on my MeWe page which includes any trends in total cases in the US as well as possible treatments being developed. You can add me as a contact if already on MeWe or join and add me. mewe.com/i/petersteinmetz
 
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But these models depend on knowing how many cases there are, and testing isn't consistent across regions or even day to day. If some location hasn't been testing many people, then starts testing more, it will skew the curve and make it look like cases are increasing faster than they are. Of course it will also mean there were more cases to begin with. Garbage in, garbage out.

Yes. Testing data is very noisy and that noise is non-random. Can't go into the details, but over time testing from the same area may go to different labs with varying turn-around times and testing may be ordered and processed with varying prioritization policies. So depending on when tests where sent and under what priorities, you may see sudden 'surges' caused by non-random releases of test data by the labs. If you dont have good demographic, spatial, timing and clinical data, you have no way of correcting the input for those factors. As a result, fitting any kind of mathematical curve to a non-mathematical process should be done with great care.

It seems that the only way we can gauge the seriousness of the outbreak is to look at the increase in deaths due to COVID-19, or hospital admissions of people testing positive.

And again, without the underlying demographic and clinical data, there is no way of drawing valid conclusions from that 'raw' data. We have a local case where the infection got into a nursing home that sits right on the border of three counties. All the test results were reported the same day, and suddenly there are 66 patients of which a number are going to move to the death column within the coming weeks. Most of the hospital admissions are going to be in the neighboring county. If you compare the fatality data with other jurisdictions where you have community transmission to a much younger population, your results are going to be skewed.
 
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Sure, but it cannot continue like that. Even though it's a relatively slow growing exponent, in about 9 months, that curve kills everyone on the planet and we know that won't happen. Growing at the same rate, it kills 1% in 6 months, but it will have slowed down long before that. Every curve is going to flatten eventually because the virus will run out of weak members of the herd that succumb to it. This isn't the way to analyze it, it just leads to panic.
Of course. No one is saying it will continue like that. It'll flatten eventually. It'll either naturally kill everyone it was going to kill, or we do something external to bend it. Whether it's quarantining people/populations, finding a vaccine, or whatever, it'll eventually find it's inflection point and go logarithmic. The trick is trying to get it do to that sooner rather than later.
 
You assume the virus does not mutate and then take the stronger members. Or people who have been previously weekend....
Personally, I'm previously weekday. ;)
 
The problem with the news...they make it sound like it’s gonns stay exponential...it’s not ...and it’s not asymptotic towards infinity. It will taper to a normal distribution.

Ding...ding...ding... it will follow a normal distribution. If you look at the number of new cases on the log scale, you will see it is beginning to bend over. While the number of new cases per day are still quite large, the day over day new cases is slowing down. That is the rate of change is slowing. We need to see it go negative to know we are on the backside of the gaussian distribution.

https://www.worldometers.info/coronavirus/country/us/
 
You may be right regarding people’s use of the word in common language, but I assert that increasing becoming more rapid is a perfect description of the behavior of an exponential curve, and that when the news is using it, they are quoting the scientists and doctors who are well aware of the math and know that the spread of a disease in an epidemic can be well modeled with an eponential function.

Using base 2 as an example, and restricting the x values to integers, the binary exponential series is:

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024,...

Seems to me that sequence fits both the definitions well. Mathematically, it’s

f(x) = 2^x

And it’s also increasing at a more rapid rate.

The scary thing is that if x represents some period of time, and f(x) represents the number of people who are infected (or perhaps die from) the Covid 19 virus, then we do have a serious problem...



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Yes, and if the number x above represents days, and f(x) represents the number of cases, we ARE screwed!

The rise and fall maybe exponential, but it will still follow a Gaussian function. There are many different shapes to the normal distribution depending on the exponential function to the Gaussian distribution function. Hopefully we will have one that is flatter and more distributed with time, but without preventative measures the area under the curve (number of cases) will be the same, just spread out.

https://images.app.goo.gl/7PhZwEf7VpYQ1cTJ8
 
Finally a voice of reason

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*What Would Walter Say
 
While the number of new cases per day are still quite large, the day over day new cases is slowing down. That is the rate of change is slowing. We need to see it go negative to know we are on the backside of the gaussian distribution.

A rate of new cases cannot go negative.

What we need is to get to the point where the number of new cases is exceeded by the combined number of recovered+deaths for a sustained period of time.
 
Quite frankly, I'm not so sure we're not screwed anyway. We just returned from grocery shopping not 10 miles from the largest outbreak in MD to date. Though customers seemed to be willing to do their best to maintain social distancing, store management appeared to be doing nothing. Frequently touched surfaces like checkout counters and credit card terminals weren't being routinely cleaned, checkout clerks weren't gloved, one-way aisle traffic flow wasn't being directed by arrows on the floors.

Compared with the measures the Chinese put in place, what we're doing, with larger numbers of infected, seems pitifully inadequate.
 
you are on your own to think wisely my friend.....wear a mask and gloves...and sanitize after you dis-robe. ;)
 
Quite frankly, I'm not so sure we're not screwed anyway. We just returned from grocery shopping not 10 miles from the largest outbreak in MD to date. Though customers seemed to be willing to do their best to maintain social distancing, store management appeared to be doing nothing. Frequently touched surfaces like checkout counters and credit card terminals weren't being routinely cleaned, checkout clerks weren't gloved, one-way aisle traffic flow wasn't being directed by arrows on the floors.

Compared with the measures the Chinese put in place, what we're doing, with larger numbers of infected, seems pitifully inadequate.

When I bring something home from the store. I bring it all to my back porch. I then take my shoes off in the garage, go inside and wash my hands, then wipe items down outside with a disinfecting wipe, and bring them inside.
 
A rate of new cases cannot go negative.

What we need is to get to the point where the number of new cases is exceeded by the combined number of recovered+deaths for a sustained period of time.

What I meant to say is that the day over day is negative, ie the rate of change is negative, the slope of the Gaussian distribution in negative, which means we are on the backside of the curve.
 
The problem with the news...they make it sound like it’s gonns stay exponential...it’s not ...and it’s not asymptotic towards infinity. It will taper to a normal distribution.
Huh?
The incidence curve plots number-of-cases vs time.
Distribution curves plot a measured variable vs incidence.

Cannot, just for argument sake, morph one into the other.
The ordinates and abscissas are not the same.

I’m just, for my own peace of mind, going to have to quit revisiting this thread.:rolleyes:
 
When I bring something home from the store. I bring it all to my back porch. I then take my shoes off in the garage, go inside and wash my hands, then wipe items down outside with a disinfecting wipe, and bring them inside.
I spray everything with denatured alcohol. But I've done that for years. An awesome time to be an introverted germophobe.
 
Just stumbled across this on YouTube ..... very useful and thought provoking:
 
I spray everything with denatured alcohol. But I've done that for years. An awesome time to be an introverted germophobe.

Yeah, but being hypochondriac is somewhat problematic.
 
We just had the first confirmed case in the county announced yesterday. Methinks they jumped the gun on the rural areas, we've seen nearly zero corona and about the time they inevitably have to end the shelter in place stuff is probably when we'll be in the middle of it.
 
We just had the first confirmed case in the county announced yesterday. Methinks they jumped the gun on the rural areas, we've seen nearly zero corona and about the time they inevitably have to end the shelter in place stuff is probably when we'll be in the middle of it.

Note: This is based on news reports and public health specialist opinion pieces.
There are enough people in the rural areas who work/commute/visit the larger cities; that it will come. It is just a matter of time. Further, most rural area medical centers are not truly equipped to handle complex cases. More often, the rural hospitals stabilize patients and send them on. Therefore, rural hospitals are often affiliated with larger hospitals in metro areas. Often many hours distant. The result, if the larger hospital does not have capacity, the rural hospital will be in even worse shape.
The resulting conclusion, lock down the rural areas also, this will delay the time till the virus appears in the rural area. This may give the larger hospital time to "flatten the curve" and then have the resources available to help the rural area when it hits.


Tim
 
Though this was interesting


Restrictions Are Slowing Coronavirus Infections, New Data Suggest
https://apple.news/ANPrDafCtTy6-o2SzlgX67g
Interestingly, I was just playing with the covidly dash stats and if you sort the states by infection rate per million you find California has fared well, it's in the company of more rural areas like Maine, Wisconsin, Alabama, Missouri, Montana, South Carolina.. etc. Impressive for a state that has LA and San Fran.. you would expect rates closer to New York. But it appears the swift measures taken weeks ago at the county level had a positive effect

NY is apparently having FEMA bring in refrigerator trucks so they can store the dead.. crazy stuff!

There's an economic impact for sure, and there's a philosophical argument in there somewhere. But objectively the shelter in place rules work... and the truth still stands that if you locked everyone at home for 14 days this would disappear and we could be coming out the other side of this that much sooner

upload_2020-3-30_20-59-31.png
 
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