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4/25/20 1:08 P

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Normally they want to bring your own re-usable bags. Right now they don't want them in the store, ... don't bring potentially contaminated bags into the store.

So they only put groceries in the the usual store provided "single use" plastic bags.

James
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4/25/20 12:46 P

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James that sign...i'm not sure i'm interpreting right? does it say you shouldnt bring your own bags? what are you supposed to use?

Holly
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4/25/20 12:33 P

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Outside my grocery store:


James
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4/25/20 10:17 A

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I did that math on a few states and countries. I took the number of confirmed cases, multiply by 30 ... assuming that about 1 in 30 are the ones who need hospital care at some point and are tested and confirmed, and divide that into the population of the state or country:

N.Y. state: 2.3
Florida: 23
Georgia: 16
California: 32

That means this, in California for every person who has caught the virus, there are 32 who have not yet. In N.Y. for every person who has 2.3 who have not. etc.

Canada; 29
Australia: 125
USA as a whole: 12

Edited by: -JAMES- at: 4/25/2020 (10:19)
James
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4/25/20 1:02 A

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I hope so too but I’m afraid you are right.

Holly
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4/24/20 10:34 P

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I just found a Wikipedia page that documents corona virus cases in the US state of Georgia.
Here is that page:
en.wikipedia.org/wiki/2020_co
ronavirus
_pandemic_in_Georgia_(U.S._st
ate)


Someone obviously updates this page everyday as it has a whole history of active cases.
A week ago on Friday April 17 it was 16764 active cases, and today April 24, a week later there are 21592 active cases. 21592/16764 = 1.288. Doing a little math I find the number:
X = 1.0368
this is the factor that when you multiply 16764 by X seven times for the week, you get to 21592. So the daily compound growth rate it 3.68%. I'll return to that Wikipedia page in a week and after that too, and see what has happened.

I don't expect to see any real change in the next week, it would surprise me. The period of having the virus and being symptom free is about 5 days. But about a week from now we may see something.

I really hope that things work out well for Georgia, if it works out not too bad, then it is the start of a path back to more normal living. Probably with changes, but more normal.

I'm afraid for them though. Assuming that about 3% of the people infected are the ones that go to hospital and end up in the statistics, this means that about 720,000 are actively infected right now. The population of Georgia is about 10,600,000 so that makes one person in 15 being sick right now.

I hope I've made a mistake with the estimates.

Edited by: -JAMES- at: 4/25/2020 (00:43)
James
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4/24/20 2:32 P

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i'm so sorry about your sister in law. thats such a tough thing. sounds like she has a sense of humor though!!

I had heard rumblings that getting the virus did not guarantee immunity, but until i saw the article i posted, and others like it, i wasnt about to say anything. but its been confirmed, and there are more. the one good thing is the symptoms arent as severe the second time around, from any that i've heard about. we can only hope....

think about chicken pox. i remember people bringing their kids to my house when i had it so they could "get it over with" only....now they get shingles, because they had chicken pox. so that was no immunity either...just a different form. i'm wondering if its the same thing..you can get it again, but in a different form or in a milder version.
purely speculation..i'm not a doctor and dont profess to know if that is a possibility or truth..just a wondering in my mind.

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4/24/20 2:26 P

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NIGHTSKYSTAR,
... OH NO!

That really makes things awful, and complicated.

My sister-in-law in Germany was just talking to my wife. She is at home on palliative care, ... she has terminal lung cancer and no treatment will cure it, perhaps prolong her life by a few months, but the treatment is as bad as the disease. You feel awful, worn out, etc. from the treatments, so she is just taking the days as they come.

Anyway, the home care nurse tells them that she tested positive for corona virus, but has now recovered. Sounds like a bad scenario. Then my sister-in-law and her husband remember that they both got really sick from out of no where in February, before the nurse even visited, and looking back at the symptoms, maybe they both had it at home. She's been on disability at home for about 1/2 year or so, and her husband retired in January. I was thinking its the old retire and get sick thing once the stress is off. But both of them worked in a hospital, maybe he brought it home just as he was retiring.

Anyway, my wife's sister says to the palliative home care nurse, ... I think we are OK, ... we probably gave it to you !!!


James
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4/24/20 10:21 A

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Unfortunately, James, thats incorrect. here is an article about a couple that was positive, recovered, went to donate blood (as some thought possibly there would be antibodies due to them having had it) and are now positive and sick again.

www.poughkeepsiejournal.com/story/ne
ws
/local/2020/04/17/coronavirus-after-R>recovery-new-paltz-couple-tests-posi
ti
ve-again/5152545002/


they arent the only cases that have had repeats. One of our corrections officers has been very ill with the virus. they had to put him in an induced coma when they put him on the vent. hes 40, 5 kids...and he had to be taken to a larger hospital..and the prognosis was not good. But he came home yesterday..with the warning he could re contract it if he doesnt stay away from everyone. he is quarantined in a room by himself, at home.

its scary as all get out..and they are hushing this stuff up..but china has also seen many get it again.

Holly
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4/24/20 12:37 A

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Looking at the strange future.

Looking at cases in the USA in the last three weeks (which is a long time), the number of active cases is growing, but linearly, which to me is strange. Active cases have been going up by about 30,000 people each day, the same as the number of new cases each day.

Now people should leave the active pool in about 2 weeks. But I don't see that happening.

Very puzzling to me that the growth is a rather consistent 30,000 a day. Assuming 3% of the cases end up in hospital and a making the statistics, tha means about 900,0000 people a day in the USA actually get sick with this virus.

This means, that if this linear graph kept going, it would be about a year to cover the whole USA.

I suspect that almost any country will have to open up before the virus has run its course at such a pace. However, I think things will change to slow down the spread. Stores will have a maximum number of customers at the same time. My local grocery store, which is rather big, has a limit of 25 customers (I asked the person at the door who counted as people came out and kept control of who when in).

I think these sort of queue's, and changes to seating in restaurants, and a whole host of other social distancing efforts are going to continue for a long long time, many many months.

Slowing down social interactions and modifying how we do things (like limiting number of customers in a single location like grocery stores) will do these things:
- lower the peak of people sick at the same time, which allows hospitals to deal with the peak
- slows the spread down, but makes it last longer, perhaps much longer, like a year or more
- buys time for a vaccine

I'm not putting great faith in a vaccine. Not because I don't think it can be done, but rather because if one is created, it will take a long time.

Perhaps antibody testing for this virus will be found, and those who had the virus and now have the anti-bodies and presumably don't spread it any more, or can't get sick again, can get a sort of "passport" certification. They can work in public places like restaurants, or stores, etc.

I know that there is some thought that one might get sick with this virus more than once, or make people sick even after recovering. If that is true, then the whole human race is in deep deep trouble. I don't think this is likely.

Edited by: -JAMES- at: 4/24/2020 (02:45)
James
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4/22/20 11:34 P

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URBANLOTUS,
I just looked at the graph of cases for Australia. Still going down on active cases. Back to where you were a month ago, on the way up ... but now on the way down!!

What is your country doing? Looking great. Is Australia talking about opening up the economy, or social interaction? Or opening up under control? I'm envious.

James
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4/22/20 1:02 A

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As much as I like using mathematics to understand things, at this point I find it not very useful for corona virus.

Australia for example has a very strange trajectory in number of cases. Even the US, when taken as a whole, has been very linear in the last week. Roughly 28,000 new cases a day, virtually a straight line. I keep looking for the inflection point where it turns down, but not yet.

NIGHTSKYSTAR, at this point, when anyplace opens up, the number of cases has to go up, the question is how much, and how long. I think the USA state of Georgia will provide an example. They've decide to open up things. If in two weeks their numbers have jumped up by a lot, then the world will know that isolation is still the thing to do. But it things are under control there (more or less) then isolation may not be as needed as one might think.

I feel sorry for the state of Georgia in the USA, ... used like an experiment. It its not as bad as one would think, ... great, we'll all learn and have a clearer path forward. It in 2 or 3 weeks its out of hand and their hospitals can't manage the critical cases, too bad for them, and we will have learned too.

Edited by: -JAMES- at: 4/22/2020 (13:45)
James
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4/20/20 9:28 A

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oh Susan thats wonderful with zero new cases!!

there was a couple here who went to donate blood that had been very sick with it in early march. they both tested positive so couldnt donate, and have all symptoms again, but they did say its milder and they arent as sick as last time. but proof positive..and i saw a news article last night that not only have the proven that you can get it again, but that heat does NOT destroy it (our president had said it would disappear as soon as warm weather came. total ignorance..you dont say things if you arent sure.)

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4/20/20 1:22 A

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There is a myth here too that recovering form a bout of COVID-19 grants you immunity. The media is going along with that. Dr friends say what you are saying, Holly, that you can catch it repeatedly.

Yes, you are also right that we have a nation wide social isolation lock down happening. States are all getting different results as the borders are all closed too. Today in my state, there were NO new cases in the last 24 hrs. Everyone knows that is not the end of the story, but it caused a few smiles today.

Susan

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4/20/20 1:01 A

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Interested to see James’ prediction on this. Personally I think if we open too early it will get worse. Getting it does NOT give you immunity. So people can get it again. I’d rather stay in all summer and be done with it than jump the gun and be in till Christmas

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4/20/20 12:09 A

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What is your expectation about a second or third wave as we begin to loosen restrictions, which must eventually happen?

Rhonda



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4/19/20 5:24 A

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Lotus I think the difference is, if I’m not mistaken? You have a countrywide rule. Here we have some states distancing. Some not. Florida opened beaches yesterday. The pictures made me sick to see..people shoulder to shoulder no protection—what’s that state going to look like in 2 weeks? And how many will leave the state and take it with them?
If everyone doesn’t do it it’s not going to be over anytime soon. So sad..and saddest is Florida’s high number if really vulnerable population.
News story yesterday from my state—older couple very sick with it early March but fully recovered. Went to donate blood as there was an emergency call for it. Apparently all donating downstate are tested—both were denied as they have it again—and sure enough their symptoms are back as of the date of the story. You can get this again...more and more people are—they think they are immune but that’s not true.

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4/19/20 12:26 A

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For the USA, since that last picture the total cases bent up again, so the apparent inflection point was not really it.

Just today 515,561 = F(t) for active cases. If we are at the inflection point today that that is F(t) and dF/dt is totay's active cases minus yesterdays, so the change in active cases, and divide that into active cases to get an estimate of the width of the peak. and that is about 21 days.

So 21 more days to the national peak, and another 21 days coming down back to about where we are today. So 42 days from now. But seeing an inflection point in the data today is hard to see. In other words the inflection point may be yet farther in the future, and the peak yet wider.

If you relax social distancing less than 42 days, but a higher peak.

The math for the height of the Apex words out to the height of the inflection point times the square root of e, so time about 1.65. So if we are at the inflection point in the USA right now, 631,000 cases times 1.65 means about 1,041,000 hospital cases at the apex. Assuming 3% of the cases end up in hospital, that means about 34 million Americans sick at the peak. About 10% of the population simultaneously sick.

Edited by: -JAMES- at: 4/19/2020 (00:37)
James
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4/19/20 12:08 A

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Well tanh() and all that was only partly successful. I initially avoided a Gaussian because the math was just too ugly, and probably not super accurate anyway.

I had a good nights sleep and had some inspiration, then yesterday a nap mid afternoon and both resulted in insight on a Gaussian curve ... here it is:

F(t) = A exp ( - ( (t - a) / w ) ^2 )

So that funny ^2 means squared, or times itself. exp(x) is the natural logarithm base, e = 2.71828 .. to the power of x.

t - is time in days,
"a" - is the point presumably in the future when the peak is reached
w - is the standard deviation, or width of the peak.

If (and this is a big "If") the data fits a Gaussian curve, then:
A = F(t) * (square root of e) = F(t) * 1.65...
In other words multiply the value of F at the inflection point by about 1.65 to know the value of F at the peak.

The second thing is that at the inflection point:
w = F(t) / dF/dt

That is divide the value at the inflection point by the rate of change of that value, and that is the standard deviation, or width of the peak in days. If you do the same calculation for w before the inflection point you get a value, but it is smaller than the width. In other words you can get a lower estimate on how wide the peak will be.



James
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URBANLOTUS's Photo URBANLOTUS Posts: 4,089
4/18/20 11:08 P

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James, we ARE social distancing here in a big way, but there ARE still numbers of people out there in public sans masks/gloves. So it is strange and interesting to see the way the curve is playing out here.

As for what we might be doing differently:

We have been told the social distancing will continue for the foreseeable future.

Over 65s are told not to shop - to order things and get them delivered to their homes.

The numbers being reported could be wrong. Not everyone healthy is being tested, and not everyone with symptoms is being tested either. A friend has pneumonia and other symptoms. She was not tested when she went to a respiratory clinic. She was sent home to isolate herself from family in the same house.

The borders of every state and territory are closed. Air travel is out, except for Aussies returning home, then they go straight into social isolation in motels for two weeks.

I don't really know what is different about our restrictions, or even if they are all that different.

Here are the official numbers in Australia:


www.health.gov.au/news/healt
h-alerts/n
ovel-coronavirus-2019-ncov-h
ealth-
alert/coronavirus-covid-19-curre
nt
-situation-and-case-numbers
3

I have not seen an official curve the shape you showed. Something does seem off, somewhere.

Edited by: URBANLOTUS at: 4/18/2020 (23:09)
Susan

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4/16/20 11:43 A

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Some of my math results are "breaking down". Though I do see why Australia is not working out ... those folks have done something unusual to change the infection rate the way they have.

I'm still going to update this post ...
------------------

Here is an picture of "active cases" in the USA


Just "eyeballing" that. This curve is obviously going up. However one can look at when it is getting steeper and steeper up, and when it starts to get less steep. That point is called the "inflection point". On the USA graph here, that looks to be around April 14, just near the most recent points. It just starts bending down a bit, ... looks like it.

- - - - - - -
Italy:


For Italy that inflection point where the curve starts bending down rather that up is around March 31, and just "eyeballing" the peak for Italy, about two more weeks, April 30.

- - - - - - -
Spain:


For Spain the point at which it start bending down look like around March 31, and the peak looks to be right around April 16.

Here is my numerical analysis assuming 1 in 30 cases ends up in those hospital statistics, and that the others handle things at home. Just plunking in the total cases data from two recent days:

- - - - - - -
Australia:


Australia has obviously done something like social distancing in a very serious way staring around the end of March, to have such an impact to a greatly growing rate before that. The shape of their curve is not at all "natural".
- - - - - - - -
I put the total cases pair of numbers for total cases April 15,16 and the populations of each area, assuming 1 in 35 people end up in the hospital in the statistics, and stay in the hospital for 2 weeks and here is what came out:

NY State: peak in 6.4 days, width of peak 31.4 days, peak in hospital 61062
USA: peak in 54.2 days, width of peak 42.5 days, peak in hospital 762372
World: peak in 104.3 days, width of peak 45.5 days, peak in hospital 16573947
Canada: peak in 60.1 days, width of peak 33.9 days, peak in hospital 109402
Australia: peak in 1433.1 days, width of peak 610.4 days, peak in hospital 4095
Germany: peak in 122.7 days, width of peak 88.1 days, peak in hospital 94031
Italy: peak in 89.4 days, width of peak 80.5 days, peak in hospital 74835
Spain : peak in 68.1 days, width of peak 74.3 days, peak in hospital 62903

While the NY State peak prediction looks right, as Cuomo was surprised recently that the peak seemed just a few days further out than expected, and wider than expected, ... the others seems to have a peek much too far out, like Italy and Spain. Looking at the curves, peaks 2 or 3 months in the future just don't look right.

Australia's number looks just wrong, a peak about 4 years from now (1433 days) ... just wrong. Well they have a population of 25 million, and given the small fraction of the population currently infected, they should be on the way up, but are on the way down. So those numbers in the same "model" just produce crazy numbers. Australia is doing something unusual to control the spread.

Conclusions...
- My math model has broken down and I'll stop using it
- Eyeballing the curve for a particular area is the best a non-expert can do
- I will post graphs of areas (countries, states ...) in the future






Edited by: -JAMES- at: 4/17/2020 (08:55)
James
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4/15/20 5:08 P

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You’ve been very close in your calculations so far..

Holly
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4/15/20 4:03 P

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These calculations are not for the faint of heart...

- - - - - - -

I did the math, some integration of currently infected, and looked back 2*D days actually 2*7, days, or two weeks.

I assumed that each hospital case was in hospital for 2 weeks. I assumed that only one in 30 cases would end up in hospital and the people in hospital at the same time at the peak is:

(1/30) * 327,000,000 * tanh(aD)

If "a" gets smaller, that "flattens the curve", the peak is not as high and tanh(aD) is smaller as "a" gets smaller. The larger the number of days in hospital is, that 2*D the more overlap of simultaneous folks in hospital at the peak.

tanh(aD) = 0.163702 a=0.023598 D=7

So at the peak the fraction 0.16 of the population will be simultaneously sick. That is 16% of the population sick at the same time. This will happen around mid June, June 15, 60 days from now. Now that is 327,000,000 * 0.163702 = 53 million ill with corona virus at the same time. Now not all of those people will be in hospital, 1 in 30 will be, so about 1.75 million, or about 1,750,000 people in hospital. Right now there are about 550,000 active cases. So at the peak in mid June three times as many people as are currently in hospital.

- - - - - -
Increasing social interaction (reducing social distancing) will only move the peak sooner than 60 days, and make it higher (though narrower). I hope my calculations are somehow wrong, but I don't think so.

My calculations for Italy with this based on 101739 total cases on May 30 and 105792 on May 31, and the population of Italy, and assuming 1 in 30 people end up in hospital:

Italy: peak is 71.5 days in the future, width of 49.5 days, peak


Now 71.5 looks to be too far in the future, same with the width of the peak. But the maximum number of folks in the hosptial at the same time (population of italy / 30) * tanh(aD) comes to 141,000 and that looks a little high too, but not crazy high, not even a factor of 2 off.


Edited by: -JAMES- at: 4/16/2020 (11:59)
James
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MAR_V3's Photo MAR_V3 Posts: 1,206
4/15/20 7:12 A

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Hi James, I'm proud of my boss Dr.Amy Acton. Ohio's quick and decisive response has flattened the curve. Go Public Health!! Our Epi's rock!!

https://coronavirus.ohio.gov/wps/portal/
gov/covid-19/dashboards/forecast-model

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I decided to look at a country where their apex has been reached, and the country is Spain.

www.worldometers.info/coronav
irus/#cou
ntries


From this link you can find Spain and find this graph:


I put in the data, not of active cases, but total cases, which is what its input is:
35,136 for March 24
42,058 for March 25
46.9 million population of Spain.

What it said was 18.5 days to the peak, width of the peak 11.9 days.

18.5 days after March 24, 25 is indeed pretty much April 13 as the model predicts. Looking at this graph and the estimated 11.9, OK 12 day width of the peak looks about right too. Sadly that looks like about 12 days before the peak, to 12 days after the peak, not 6 days on each side.

Next thing I'll try to add to the calculation is number of cases at the same time, so I can estimate the height of the peak, and the Spanish and probably Italian data will test that estimate.

Edited by: -JAMES- at: 4/14/2020 (12:00)
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I put those formula into a computer program. It makes running the numbers for different countries easier and less error prone. What I use is number of cases in hospital on two dates, usually one day after the other, the area (or country's) population, and the estimate that one case in 30 ends up in hospital. So here is my more recent analysis:

NY State: peak is 18.2 days in the future, width of 43.1 days
USA: peak is 60.7 days in the future, width of 42.4 days
World: peak is 130.0 days in the future, width of 53.4 days
Canada: peak is 75.0 days in the future, width of 38.8 days
Germany: peak is 168.2 days in the future, width of 111.8 days

I ran numbers for Australia, but it came out very strange. I need to double check.

As you can see, with New York State peak 18 days in the future, and a width of that peak being 43 days, that area is well into the high hump of cases. For the US to look at New York and say "the worst is over" is wrong ... it is almost over for New York State, but country peak is mid July, and wide enough to cover end of June, all of July, and start of August.

Edited by: -JAMES- at: 4/14/2020 (10:42)
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4/13/20 10:28 A

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cdc.gov has some good information too.

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I found a page on wikipedia for corona virus numbers and many countries in the world:
en.wikipedia.org/wiki/201920
_coronavi
rus_pandemic


From there I drilled down and found numbers for New York State, where NIGHTSKYSTAR is, and found them on Wikipedia:
en.wikipedia.org/wiki/2020_co
ronavirus
_pandemic_in_New_York_(state)


Number of confirmed cases
April 10: 170,512
April 11: 180,485

Edited by: -JAMES- at: 4/12/2020 (10:22)
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That’s good news!

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For the corona virus, I've changed my estimate from one person in ten who goes into the hospital, to one person in 20 who gets ill ends up in hospital. The other 19 either get the virus, and have no symptoms, or maybe minor symptoms, or more, but not enough to end up in hospital.

Rather than a more difficult Gaussian curve, I found this one discussed somewhere:
tanh( at + b)

I saw a math forum where someone had a Gaussian problem, but it was too hard to solved (yup it is) and wanted a similar function, but easier to solve.

A hyperbolic tangent function. "a" and "b" are constants, t is time (in days) and the tanh() functions is -1 far far in the past, and around at+b =0 it gets larger and smoothly crosses over to +1 as time gets larter and larger. This function gets larger quickly in a brief time and has a similar quality to a spreading infection. A slight adjustment to this function:

EQN. 1: F(t) = ( 1 + tanh(at + b) ) / 2

F(t) is the fraction of the population exposed to a disease. It starts off near at much earlier times, and much much later, at large t everyone has been exposed.

The crossover area from where few have been exposed, then all the activity, then after that nearly everyone has been exposed is near (at + b) = 0. The width of the crossover is roughly 1/a days. The peak of the spreading is around when (at +b) = 0

The F(t) function has the right qualities for a spreading infection, nothing much for a long time, then it spreads like crazy, then it has finished spreading.

Making yesterday t2= 0 and the day before yesterday t1= -1
one can first solve for "b":

EQN 2: F(t2) = (1 + tanh( a*t2 + b) ) /2

We know that F(t2) was 502,876 cases in the USA total so far. Cases that made it to hospital. I'm assuming the real number is 20 times that. So 19 folks either have no symptoms, or have symptoms but not bad enough to end up in hospital. Population of the USA is about 327,000,000

So the fraction of people exposed in the USA up until yesterday:
EQN 3: F(t2) = 20 * (502,876) / 327,000,000 = 0.031 = (1 + tanh(b) )/ 2

That 0.031 number would mean about 3.1% of the US population has been exposed. Not precise, but a good guess.

A little manipulation and:
EQN 4: tanh(b) = -0.938
and
b = -1.72

Since "b" is negative, it means the peak in cases is coming in the future. With only 3.1% of the population exposed so far, it makes sense that the peak is still coming.

Now to figure out "a". If you take that equation, and take its derivative with respect to time (something from calculus):

EQN 5: d F(t) / dt = d (( 1 + tanh(at + b) ) / 2 ) / dt

This is the time rate of change of the quantity, how much does it change from day to day

For example, if F(t) is how much of the liquid is in bottle, d F(t) / dt is the rate that it is filling up, the rate of change of the quantity.

If you have had a calculus class then you know, or you can figure this out:
EQN 6: d F(t) / dt = a* ( 1 - tanh(at+b)*tanh(at + b) ) / 2

The rate of change on the left is known from 469,124 on April 9, to 502,876 on April 10, subtracting those, up 33,752 in a day. Assuming 20 times that is how many people got infected in one day (remember I assume only 1 in 20 made it into the hospital statistics)

So probably 20*33,752 infections up in one day, and the population of the USA is 327 million, so the rate of change of the fraction of people who are exposed today is:
EQN 7: d F(t) / dt = 20 * 33,752 / 327,000,000 = 0.002 = a* ( 1 + tanh(at+b)*tanh(at + b) ) / 2

Then plunking the value of tanh(at+b) today, which is in equation 4, it is -0.938

0.002 = a * ( 1 + (-0.938)*(-0.938) ) /2 = a * 0.06
EQN 8: a = 0.033

So what the heck does "a" mean, or this 0.033 imply?

So since the formula has (at + b), 1/a = 1/0.033 = 30 is the time scale or width of the peak in days, which is about 30 days. So you'll be close to that peak value for about 30 days, say getting "close" 15 days before, reaching peak, then coming down, but still being high for the next 15 days. This is not a surprising number ... people who recover from the corona virus do take a few weeks to recover and be out of hospital. 15 days, two weeks or so, yes a very realistic number.

Now to use the values of "a" and "b" to figure out when the peak itself is, and that is when (at + b) is zero

EQN 9: days to peak = -b/a = 1.72 / 0.033 = 52.12

OK Peak number of cases in the USA in 52 days, pretty much the end of May. The peak is about 30 days wide so high number of cases from mid May (15 days before peak) to Mid June (15 days after peak).

- - - - - - -

Not every area is impacted at exactly the same late May period, that is just the high point for the country as a whole.

- - - - - - -

I looked at the only two numbers I could find for New York City .... I really wanted New York State, .. maybe I'll find them, but I lost the link. Anyway I found two numbers of NYC, 60,850 on April 4, and 64,995 on April 5. Population of NYC 9,400,000

So still growing, and peak in the future. Now the good news for New York City, from those two data points, fitting that curve gives:
a = 0.071
b = -0.85

So width of the peak for New York City is about 1/a days, or 14 days. The peak is in the future - (a) / (b) days, which is about 12 days from April 5, so peak around April 17. So this week. The 14 day width of the peak means .... about a week to the peak 17, and a week on the other side. So about April 24 and we will be where we are now, but the number in hospital going down.

So yes, this is the sort of information coming from Gov. Cuomo , ... and I agree !!!


Edited by: -JAMES- at: 4/12/2020 (02:27)
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you are so right Charlene. they dont get counted. and that skews everything..

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Been thinking, the stats are only given are those people who are given a test, which is. of course, the only way they can do it.

But, what about the thousands more people who have the virus and have gotten over it already.
I think this brings the numbers up significantly.

A friend of mine was sent for the test (fever, body aches, dry cough - asthma challenged). They did not give her the test and sent her home saying she has the virus. I don't think she was counted or people like her counted either.......

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I posted at the end of the month that the peak in cases looked like in about 2 weeks, so around the 14-th of April.

Just yesterday I did analysis with fitting the data with a tanh() hyperbolic tangent function rather than a Gaussian. I'll post some details later. Its just fitting the data with a function with the right attributes ... starts at 0 (nobody infected) grows to 1 over time (everyone exposed). Its not exact, its qualitative. It uses two inputs, fraction, or number of people currently infected, and a second input of how much that number grows per day. Those two bits of information then are extrapolated.

I'll double check the estimates, but not one week from now to a peak value, but many weeks, about 8 weeks.

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4/8/20 3:07 P

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Holly, I didn't know about that musician, but I saw his name go across the ticker at the bottom of the CNN station earlier today. Too bad.

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very saddened today with the loss of John Prine to covid-19.

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https://www.youtube.com/watch?v=M5azNpTwVk
8

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NIGHTSKYSTAR, *sigh* ... yes.

Right now for the state of New York which has the most people who tested positive so far is 131,916

Assuming 10% of the people who get the virus end up in hospital, and test positive, this means that ten times 131,916 or about 1,319,160 have been impacted so far, about one seventh of the population.

So numbers go up by a factor of 7 for New York state.

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4/6/20 8:12 A

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thanks James. my estimate was much higher than Dr Fauci's. hoping i'm wrong and hes right, or even overestimating!

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Comparing this corona virus to a seasonal flu ... just to get a feel for the numbers.

Well ... I'd like to think its nothing ... nothing more than a bad cold. But as near as I can tell here is what the facts are...

www.webmd.com/cold-and-flu/fl
u-statist
ics


That page the information on the common flu can be looked at this way:

So in the US each year something like this:
- 1 in 10 get the flu (10% of the people get the flu each year)
- 1 in 1600 end up in hospital (200,000 people in hospital due to flu)
- 1 in every 30,000 die of the flu each year (12,000 people die)

In comparison for this corona virus
- everyone gets it (not 1 in 10, ... everyone, some may have virtual no symptoms but they get it)
- 1 in 20 end up in hospital end up in hospital (16,350,000)
- 1 in every 1600 die ( using Fauci's 200,000 predicted deaths)

So 1 in 30,000 die from a normal flu each year. But this one will be 1 in 1,600 about 20 times more deadly. Well yes, you can say only one in 1,600 ... but 20 times more deadly means that for the ones that survive it is probably a lot rougher while being sick.

Looking at your social circle, people you know reasonably well, let's say it is 100, either relatives, or work colleagues. Let's just call them all "friends". So chances of someone you directly know dying are not that great. Friend circle is 100, but it is 1 in 1600 who die. But friends of friends, that is 100 times 100, it is 10,000 people, and in that circle about 3 people will die. If it isn't someone you know directly, about 3 people in your circle of will loose a friend of theirs.

Looking at the ordinary flu, your friends of friends circle of 10,000 is still not as big as 30,000 so you in all likelihood won't find that 1 in 30,000 who die of the ordinary flu every year.

I hope Fauci is right with the 200,000 deaths in the US.

Edited by: -JAMES- at: 4/6/2020 (02:31)
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I went into my garage, I have a number of "dust" masks for doing renovations ... what do you know, three N95 masks.

I have a friend who is a nurse. We had a video chat through FaceTime,

So putting a mask on, ... wash your hands first, then put the mask to your face, two straps in front. Then the bottom strap goes up and over the top of your head first, and all the way down to your neck. Then the top strap up and over your head, but stopping at the upper round part of the back of your head.

Also bending the little metal clip around the top of your nose, starting on the bridge of the nose and working outward. The entire mask is supposed to form a tight seal so that when your breath in air does not leak in around the side of the mask, but comes in through the paper part only.

Taking one off, ... wash your hands first, and when taking it off don't touch the paper part of the mask as they are potentially contaminated on the outside. Reverse order on the straps. Touching just the straps, taking the upper strap off first, leaning over the Tupperware container so that when the mask falls, it falls into the container without you touching anything but the straps. Then upper strap off as the mask falls. Let sit in the open Tupperware in an isolated place for 72 hours to dry out and for any potential virus to die .. then re-use after that. At the end of taking your mask off, wash your hands again.

The virus dies when not in water, i.e. when the water vapour evaporates.

Edited by: -JAMES- at: 4/5/2020 (23:41)
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3/31/20 5:19 P

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James thank you... some great data in these charts. You can bet I'll be referring back to them in the coming days... can't wait to see a leveling off, followed by a decline. Like you and Holly, I'll be limiting all public outings. I appreciate the info and the peace of mind of your estimation.

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i guess, in times like these, i'm lucky to live and work alone. truly, my days arent much different than before, with the exception of my weekly shopping trip, which is now once every 2-3 or 4 weeks till this is over. other than that life in hollyville isnt much changed.



Edited by: NIGHTSKYSTAR at: 3/31/2020 (11:36)
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I enjoyed the challenge of trying to understand the spread. It exercised my mathematical background.

I'm very happy that though I'm still seeing gloomy things on the new (since cases are still going up), that I know the time-scale for them to turn around and go down, and I wanted to make folks not be fearful that everything is going to collapse, but the amount of time it will take to get back to normal.

I'm out on an acreage, very isolated, ... and I've been thinking for how long will I stay super isolated. Knowing how long helps my morale.

I've been looking at statistics from this site, for the US its here:
www.worldometers.info/coronav
irus/coun
try/us/

You can get to the world from that link, but here is the world, and you can click on the country of interest:
www.worldometers.info/coronav
irus/#cou
ntries


Edited by: -JAMES- at: 3/31/2020 (11:39)
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3/31/20 9:50 A

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Thanks for all your hard work.

Also, thanks for summing it all up - I gotta admit I did get lost looking at all the charts and numbers!

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On the human side what do all the numbers and calculations mean?

It means that growth of cases is not going to grow out of control and overwhelm the whole USA. Its going to grow at the present rate for at most about 2 weeks, then active cases will be on the decline.

Has the isolation helped, ... yes I'm sure it has, otherwise the peak wouldn't be 7.3 plus 7.3 days wide, it would be narrower and the peak number of people ill at the same time would have been higher, overwhelming the heath care system even more.

Stay safe!

Edited by: -JAMES- at: 3/31/2020 (11:00)
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If you don't know it, I have a Ph.D. in theoretical physics. Lots of math. As they say, "when you have a hammer everything looks like a nail" i.e. you try to use that hammer to solve every problem.

Turning it a bit on its head, Adam Savage (from Myth Busters) said "every tool's a hammer".

So I'm going to use my hammer. The actual equations I cooked up started to look like this:
R(t) + A(t) + N(t) = M
M is the population of the USA (327 million)
R(t) is the number of resolved cases, people who got it, but no longer have it either because they recovered, or sadly because they may have died

A(t) is the active number of cases
N(t) is the number of people note yet impacted

People flow out of the active pool at a certain rate that is proportional to the number of people in that group, and from a differential equation this looks like this:
d R(t) / dt = a A(t)
That is the resolved pool rate of growth is some proportionally constant times the number of active cases A(t).

It gets worse for the growth of the active cases:
d A(t) / dt = k A(t) (M - N(t))

The rate of growth of those active cases is proportional to both the number of active cases, A(t), i.e. the more active cases you have that faster you infect others, but also you need new people to infect and that pool of people (M - N(t)) gets smaller with time.

In the end the equations are horrible, non-linear, and something I didn't think I could even solve in the end.

So I had this idea. What "simple" function grows initially with some sort of doubling rate (like every three days something like that, but then over time stops growing, bends down and heads back to zero, and can it "fit" the data?

Such a simple function is this one:
A(t) = A * exp ( a*t*t + b * t)

At initial day zero A(0) = A exp(0) = A, so A is the number of active cases today, day zero. Then the constant "b" is positive and means the number of active cases grows, perhaps doubling every 3 or 4 days, but then "a" is negative and small but a*t*t overwhelms the b*t term as t get large enough and drives A(t) to zero. There is no proof for such an equation being valid, but it has the right sort of shape, it is a Gaussian curve and looks like this:


So I took data from the active cases, not total cases, but active cases:


To figure out the values of "A", and "b" and "a" I took three points 10 days ago, 5 days ago and yesterday. When you have such equations with 3 parameters you try to fit with 3 points, so I picked 3 points. The solutions of the variables came to:
13,464 active on March 19
53,697 active on March 24
136, 349 active on March 29

The values that make that gaussian go through those three data points:
A = 13,464
a = -0.0094 (small and negative, eventually drives the number down)
b = 0.325 (initially drives growth)

I picked three other points and got almost the same values for "a" and b". So what is the width sigma of the gaussian curve with those values it is the square root of 1/(-2a) which is about 7.3, in other words about 7 days growing up to the peak and 7 days coming down. The peak is at -b/2a which is 17, so peak at 17 days from now.

So this means the most active cases occur about 17 days from now and the with of that peak is about 7.3 days before to 7.3 after. Indeed another graphs supports that idea, and the Gaussian curve

The daily new cases does look like a ramp up over about a week, hit a peak then start coming down.

So I think I'm calculating the time scale about right. OK .. so this is daily new cases. The rate of them coming starts going down in about 2 weeks. But then how long do people stay sick? The answer to that seems to be about 2 weeks also.

CONCLUSION:
So numbers of total cases will keep going up, but more or less linearly for 2 weeks. Then the rate of new cases coming in will be reduced.

So yes higher and higher numbers will be reached, growing by about 18,000 new cases a day, but not crazy out of control numbers, not doubling every 4 days.

Active cases then go from about 160 thousand (currently), growing by 18,000 a day for 10 days, so maximum active to about 320,000 active maximum, then turning slowly downward.

Then since it takes about 2 weeks to resolve, those active cases will start dropping after that as not as many new ones will be coming in.

Don't panic in the next 2 weeks, numbers of active cases will keep going up, but the rate of growth of cases is linear, not out of control exponential.

P.S. ... I just saw on CNN projected days to the peak ... 9 days. Wow am I close!


Edited by: -JAMES- at: 3/31/2020 (08:53)
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NIGHTSKYSTAR's Photo NIGHTSKYSTAR SparkPoints: (739,180)
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3/31/20 7:34 A

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Thank you James!!
Jazz hands—that’s what I said haha!!

Holly
Northern NY
EDT


 Pounds lost: 141.0 
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-JAMES-'s Photo -JAMES- Posts: 14,920
3/31/20 7:30 A

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I'm focusing on covid-19 in the USA. I'm Canadian, so for me it's more natural to focus on Canada, or the world. But the USA just has a bigger pool of people, so the data has less fluctuations, its more consistent. But also world statistics are probably just too blurry and time-shifted.

A week ago cases in the USA were doubling in a little over 2 days.

It was 68,211 (Wednesday midnight March 25)

Then I predicted numbers based on doubling every 3 days (growing about 26% compounded each day):

PREDICTION BASED ON DOUBLING EVERY 3 DAYS:
Day - infections - Date
1 - 85,945 (Thursday March 26)
2 - 108,291 (Friday March 27)
3 -136,422 (Saturday March 28)
4 - 171,892 (Sunday March 29)
5- 216,583 (Monday March 30)
6 - 272,844 (Tuesday March 31)
18 - 4,365,504 (Sunday April 12)
30 - 69,848,064 (Friday April 24)
36 - 279,392,256 (Thursday April 30)

But since the population of the US is 327 million, it can't keep doubling at the initial rate, you run out of people. Its sort of like asking you to tell two friends something, and they do the same, tell two friends the message, and so on. For a while it doubles quickly, then eventually you run out friends to tell. A sort of Ponzi scheme.

Then the data came in:

ACTUAL:
Day - infections - Date
1 - 85,435 (Thursday March 26)
2 - 104,126 (Friday March 27)
3 -123,578 (Saturday March 28)
4 - 143,141 (Sunday March 29)
5- 163,844 (Monday March 30)

So these are just numbers, and 163 thousand is less than 272 thousand. But what about the "shape" of the trend?

At the start you can see it "curving up", which is looking like compound interest growing. But toward the right, i.e. more recently it looks more like a line, growing by the same number each day. So that is the first part that is good news. Yes its still growing, but linearly.

More analysis in my next post.




James
Alberta, Canada


All time highest weight : 217 pounds

Starting weight : 195.0 pounds (June 7, 2012)
Final weight : 168.2 pounds (July 23, 2013)


 current weight: 172.5 
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-JAMES-'s Photo -JAMES- Posts: 14,920
3/31/20 6:58 A

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I'm creating this topic for a few reasons.
1. - to keep you calm and rational
2. - to let my thoughts out
3. - because a lot of people are concerned

It's a crazy thing. It's very serious, people's health, and very lives may be in the balance, yet humans can find humour, even in the darkest times, it's part of their nature.

So I'll start off with a little humour. NIGHTSKYSTAR said to me that she was throwing her hand up in the air not knowing what to do. OK, something close to that. One of my high school teachers said to me ages ago, when you don't know what to do, and you throw your hands up in the air, ... just be sure to catch them on the way down.

That got me thinking ... catch them with what, your hands were "up in the air" ?

Next posts with some more serious mathematical analysis, which is point 2. As it turns out, and I wasn't expecting this I was expecting the worst, but I found 1., probably not as bad as one thinks.

James
Alberta, Canada


All time highest weight : 217 pounds

Starting weight : 195.0 pounds (June 7, 2012)
Final weight : 168.2 pounds (July 23, 2013)


 current weight: 172.5 
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