Tool for FreeBSD which extracts, curve-fits a logistic function and transposes JHU-CSSE's Covid-19 data by country

obsigna

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You'll find said tool on my GitHub repository - https://github.com/cyclaero/xcssecovid

Quick Start

svnlite co https://github.com/cyclaero/xcssecovid.git/trunk xcssecovid
cd xcssecovid
clang -g0 -O3 -march=native xcssecovid.c -Wno-parentheses -lm -o xcssecovid
fetch -qo - https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv | ./xcssecovid US - US.tsv
cat US.tsv
Code:
# Model: a/(1 + exp(-b·(x - c)))
#        a =    144036 ± 13.179 %
#        b =  0.364201 ± 2.7248 %
#        c =   64.2688 ± 0.8798 %
#   ChiSqr =  92220.86
t/d    C    L
-20    *    0.000000
-19    *    0.000000
-18    *    0.000000
-17    *    0.000000
...
...
-1    *    0.000007
0    *    0.000010
1    1    0.000014
2    1    0.000020
3    2    0.000029
4    2    0.000042
5    5    0.000061
6    5    0.000088
7    5    0.000126
8    5    0.000181
9    5    0.000261
10    7    0.000376

...
...
50    1281    792.802927
51    1663    1138.378834
52    2179    1632.871155
53    2727    2338.647108
54    3499    3342.320651
55    4632    4762.262397
56    6421    6756.478624
57    7783    9528.646839
58    13677    13327.803195
59    19100    18434.120243
60    25489    25120.832956
61    33276    33584.499721
62    43847    43848.254080
63    *    55667.801935
64    *    68495.183556
65    *    81550.592732
66    *    93997.986502
67    *    105148.182477
68    *    114592.002038
69    *    122218.258863
70    *    128143.172369
...
...
80    *    143569.151663
81    *    143711.229374
82    *    143810.103724
83    *    143878.876950
84    *    143926.695982
85    *    143959.937038
86    *    143983.040349
87    *    143999.095772
88    *    144010.252408
89    *    144018.004514
90    *    144023.390792
...
...
US.png


What the hell is a Logisitc Function?

According to Wikipedia - https://en.wikipedia.org/wiki/Logistic_function:
A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation:

{\displaystyle f(x)={\frac {L}{1+e^{-k(x-x_{0})}}}}


The logistic function finds applications in a range of fields, including artificial neural networks, biology (especially ecology), biomathematics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, linguistics, and statistics.

As a matter of fact it is THE MODEL for almost all natural growth processes, and it would be extremely surprising if not for the present spread of Covid-19 in given populations. I proved already, that the logistic function described very well the spread in China. So why not in other regions of the world as well.

What is this good for?

One very important property of the logistic function is its symmetry around the turning point x₀. That means, once a spread has been verified to have passed the turning point, we know with a probability approaching certainty how it ends up.

What is Curve Fitting?

We have a Model (here the logistic function consisting of 3 parameters). We have a time series. The curve fitting algorithm iteratively varies the parameters so that the sum of the squares of the differences between each of the simulated values to each data point becomes minimal (least squares method). In said tool, I implemented the Levenberg–Marquardt algorithm as the least squares method.

Why would we care?

Look at the results of the curve fit of the LF to yesterday's US data according to the JHU/CSSE time series - https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data

Parameter a ist the limiting value, however, since in the US we didn't reach the turning point yet (parameter c = day 64, i.e. March, 25th), the prevision of the limiting value = 144036 confirmed Covid-19 infections is yet a bit uncertain.

Now, you want to know, how your country is doing, for example Spain?
fetch -qo - https://github.com/CSSEGISandData/COVID-19/raw/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv | ./xcssecovid Spain - Spain.tsv
head Spain.tsv
Code:
# Model: a/(1 + exp(-b·(x - c)))
#        a =   70273.9 ± 8.228 %
#        b =  0.264668 ± 3.1934 %
#        c =    62.172 ± 0.91822 %
#   ChiSqr =  129867.3
t/d    C    L
-20    *    0.000025
-19    *    0.000033
-18    *    0.000043
-17    *    0.000056
Turning point was yesterday. In case there are no bigger changes in the containment measures, the spread in Spain will end up with more than 70k confirmed infections in apprx. 2 to 3 weeks.

Spain.png


I follow the time series for Germany, Italy and Brazil on my BLog - https://obsigna.com/articles/1584931539.html. Others may want to follow the spread in their country using said tool.

God help us all.
 
Last edited:
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obsigna

obsigna

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You sure all that data can be compared? Looks like there is disagreement in how to measure. https://www.telegraph.co.uk/global-...se/have-many-coronavirus-patients-died-italy/

Otherwise, good on you, nice work.
While the absolute numbers are definitely not exactly comparable, the course of the spread over the time can be compared. What I want to say is, it does not make a huge difference to me (a German living in Brazil) whether the final count of infections reaches 10k or 20k (prevision from yesterday). What makes a huge difference to me is, whether it takes 3 weeks or 3 months until the spread approaches its limit. People seem to be afflicted with the absolute numbers, and questioning whether there aren't millions of unreported cases, which didn't enter into the statistics. My answer here is, the absolute numbers do not matter to us mere mortals, as long as its course over time follows the law of logistic growth.
Somebody wrote in a comment on Z.On - https://www.zeit.de/wissen/gesundhe...tung-epidemie-karte?cid=52054033#cid-52054033:
You are healthy. -> Then stay at home!
You feel sick. -> Then stay at home!
Your test is positive. -> Above all, stay at home!
Your test is negative. -> Anyway, stay at home!
You are waiting for the test. -> Then stay at home!
You have to go out. -> Then have as little contact to others as possible and follow all the hygiene rules!
The new number of cases has increased. -> Stay at home!
The new number of cases has decreased. -> Perfect! However, for the time being, stay at home!
Given the course in Brazil, I stay at home, however, I happily do not put 10000 rolls of toilet paper on stock.
 

ralphbsz

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Fun. But obviously one has to be super careful. As Crivens already said, the data from different countries can not be compared to each other, since different countries use different definitions of what constitutes as "case", whether it's based on antibody tests or symptoms. And even within those two categories, there are many different possible definitions. As an example, yesterday the German press had many articles that Russia is (a) using an antibody test that is much less sensitive than the ones in the rest of the world, so it likely underestimates the number of cases, and (b) doesn't recognize Covid-19 as a cause of death (instead patients are considered to have died of pneumonia), so there are no deaths reported in Russia. If one can't compare data from different countries, one can also not add them.

Second, even within a single country, the testing regimen and the definition of what is a "case" probably changes as a function of time. Early on, no tests were even available; then tests became manufactured in large numbers (in some countries they are supposedly available over the counter for cash), and in other places even hospitals have too few tests available. As an example, here in Silicon Valley (one of the richest places on the planet), a friend-of-a-friend is in the hospital with a serious pneumonia, but the hospital only has 6 test kits left, so they are not even testing that patient, since the test result will not directly affect their care at the moment. So is this patient counted? Will they be counted later this week, when large shipments of test kits are supposed to arrive? If yes, will their data be backdated to when they actually started having symptoms?

And the problem is that right now, this is a very dangerous extrapolation. Fitting a logistics curve depends crucially on finding the turning point, which in turn depends solely on a small number of data points at the end. Try this for fun: take the raw data, and change each data point by +- one sigma (by sqrt of the count, since for large enough counts, 20 or more, the standard deviation of a binomial ). In theory, if there was lots of data points and the fit were stable, those changes should cancel, and the estimate of turning point position and final height should be pretty stable. I'm going to bet that right now, for most countries doing this will make the extrapolation fluctuate all over. This sort of gives you a guess of how trustworthy the results are.
 

ralphbsz

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And a specific comment about Brasil. I don't know where in Brasil you are (probably RJ or SP), but a large fraction of Brasil's population is hard to reach, hard to measure, and hard to get data on. I'm a bit familiar with the southwestern state of Mato Grosso do Sul and its capital Campo Grande: The state has ~4 million inhabitants, only one large city (which is nearly a million people), a few small cities of tens of thousands, and the rest of the population distributed all over the rural area. I bet that nobody knows how many cases there are in the rural areas. My educated guess is that there is a similar situation in Rio and Sao Paulo, with the population in the favelas receiving relatively little care, and not being well counted. The logistics curve assumes that the disease spreads through the (measured) population, causes immunity, and runs its course. In a place where a large fraction of the population is (a) not measured, and (b) only interacts slowly with the population in the big centers (not just Campo Grande and other provincial capitals, but in particular Rio and Sao Paulo, which have their own reservoirs in the favelas), this kind of forecasting becomes harder.
 
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obsigna

obsigna

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... Fitting a logistics curve depends crucially on finding the turning point ...
I know this of course, and for this reason I wrote "That means, once a spread has been verified to have passed the turning point, we know with a probability approaching certainty how it ends up."

To be sure, that we passed the turning point, the curve fitting must be repeated when new data is available. I did this with my time series analysis of the spread in China and the previsions were quite valid.

Personally, I am not interested to compare the numbers of Russia with those of other countries. Again more important to me than case numbers is, how long it takes, and according to all the data which I've already analysed, it will take 2 to 3 weeks after the turnning point was passed.
 
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obsigna

obsigna

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And a specific comment about Brasil. I don't know where in Brasil you are (probably RJ or SP), but a large fraction of Brasil's population is hard to reach, hard to measure, and hard to get data on. I'm a bit familiar with the southwestern state of Mato Grosso do Sul and its capital Campo Grande: The state has ~4 million inhabitants, only one large city (which is nearly a million people), a few small cities of tens of thousands, and the rest of the population distributed all over the rural area. I bet that nobody knows how many cases there are in the rural areas. My educated guess is that there is a similar situation in Rio and Sao Paulo, with the population in the favelas receiving relatively little care, and not being well counted. The logistics curve assumes that the disease spreads through the (measured) population, causes immunity, and runs its course. In a place where a large fraction of the population is (a) not measured, and (b) only interacts slowly with the population in the big centers (not just Campo Grande and other provincial capitals, but in particular Rio and Sao Paulo, which have their own reservoirs in the favelas), this kind of forecasting becomes harder.
I am in São Paulo, and be assured, I am following very well all the news. The Brazilian authorities acted strictly in a timely manner, when the reported case numbers were still low. For example the schools here closed at the same day on Monday last week as in Germany, however in Germany the number of reported cases were already above 7000 compared to 200 in Brazil. My wife was born in a small town in the middle north of Brazil - her mother said in a phone call, that everybody tries to stay at home, because there was reported the first case. Brazil got a public health care system which is very proactive. For example, our new daughter was born in January this year. Since then, every 3 weeks an agent of the public health care station near to our home comes visiting us, only for asking if everything is going well, and reminds us not to miss out the vaccine campaigns. I am sure that we in Brazil won't see a disaster like in Italy.
 

ralphbsz

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I get my news right now second hand. You are right that the authorities in Brasil reacted nice and early. And also the public did the right thing early on. As an example, the nursing home where my parents live (they are both very old and frail) went on lockdown voluntarily a week before any cases were reported in the city.

The other good news is that Brasil actually has a fabulously good public health system. The only problem is that the system is chronically underfunded and understaffed. For example, I happen to know that the intensive care unit (ICU in English, Intensivstation in German, and CTI in Portuguese) of the public SUS hospital in a city of 3/4 million people has 14 beds. There are two more sizeable hospitals in town (university and union of public employees), but I think their intensive care units are smaller and less well equipped (I know they send super-serious cases to the public one). In normal operation already, all beds in the CTI are occupied, and triage occurs every time a patient shows up. If they get a few thousand Covid-19 cases in the state (which seems plausible), they will be completely out of places to treat them. They key for Brasil is to hold the number of serious cases down (by slowing down infection for as long as possible), without the economic side-effects killing more people.
 

rigoletto@

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This is the last report from Russia. [EDIT] THIS is the right link.

The reported numbers in Russia are too good to be true but this is unlikely the situation is going crazy in there like in Western Europe[1], since they were the first to take measures, just after China. The border with China was locked and any Chinese seen on Russia was to be reported to be detained and quarantined.

The Russians returning from China with any suspicion of being infected were also quarantined, the ones in Wuhan were taken and quarantined somewhere in Siberia. There is the case of that women whom come from some resort, quarantined and then escaped of the quarantine.

View: https://www.youtube.com/watch?v=bFbmrZDWULg

Also, as soon the situation was going bad in some country they started to take measures of people returning from that country etc.

[EDIT] about the Russian tests.

In relation to Brazil, in particular to Rio de Janeiro specifically, just today there was a reported case in a favela. The thing is high concentrated on South Zone and Barra da Tijuca since those are the places where there are more forefingers around (tourists) and people flinging abroad often.

Most other areas have very few reported cases, often 2-4 (until now).

[EDIT] also, in favelas, at least some of them, the drug lords passed an order to everyone stay in home, and their orders are always followed because there are actual consequences for those who not comply.

[1] Central and Eastern Europe also starting taking measures earlier and are in a far better situation than Germany, Spain and Italy.
 

Alain De Vos

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I use numpy,pyplot & polyfit,polyval. It will take a week before I know if predictions are ok.
My hobby model is very wet vinger work.
The code is so small I don't think I can reduce it using R or Julia
But why would someone use C for predictive models when higher level API's are available.
And a critical remark, why would a logistic function be better than other models ?
 

mark_j

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This is the last report from Russia. [EDIT] THIS is the right link.

The reported numbers in Russia are too good to be true but this is unlikely the situation is going crazy in there like in Western Europe[1], since they were the first to take measures, just after China. The border with China was locked and any Chinese seen on Russia was to be reported to be detained and quarantined.
While I don't doubt what you're saying, the fact they stopped only Chinese seems a bit lop-sided. Surely they stopped/quarantined Russians coming from China?

Either way, you can't believe ANYTHING that comes out of China. It's hard to believe anything coming out of Russia either. Although the latter's press are a little more open; just a little.
 

rigoletto@

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While I don't doubt what you're saying, the fact they stopped only Chinese seems a bit lop-sided. Surely they stopped/quarantined Russians coming from China?

Either way, you can't believe ANYTHING that comes out of China. It's hard to believe anything coming out of Russia either. Although the latter's press are a little more open; just a little.
This was in the very early beginning when no one was doing anything outside China[1], and as I said before people coming from China with any suspicion were quarantined too, like the women of the video.

[1] China ever formally criticized Russia about their citizens being treated very aggressive. Also, Russia received a lot of criticism at that time due to they hash very measures from Western European countries...
 
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obsigna

obsigna

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I get my news right now second hand. You are right that the authorities in Brasil reacted nice and early. And also the public did the right thing early on. As an example, the nursing home where my parents live (they are both very old and frail) went on lockdown voluntarily a week before any cases were reported in the city.

The other good news is that Brasil actually has a fabulously good public health system. The only problem is that the system is chronically underfunded and understaffed. For example, I happen to know that the intensive care unit (ICU in English, Intensivstation in German, and CTI in Portuguese) of the public SUS hospital in a city of 3/4 million people has 14 beds. There are two more sizeable hospitals in town (university and union of public employees), but I think their intensive care units are smaller and less well equipped (I know they send super-serious cases to the public one). In normal operation already, all beds in the CTI are occupied, and triage occurs every time a patient shows up. If they get a few thousand Covid-19 cases in the state (which seems plausible), they will be completely out of places to treat them. They key for Brasil is to hold the number of serious cases down (by slowing down infection for as long as possible), without the economic side-effects killing more people.
You're correct, the public health care system of Brazil got by far not the ICU resources as for example the health care system in Germany. My guess is, that everybody (but a few infamous exceptions) in Brazil is aware of this and is sufficiently scared about this, and this is the reason why a vast majority of the people here does not question and supports the precautious measures.
Like a tightrope walker is much more disciplined when walking without a safety net below the rope. In the very moment, in the district where I live, the roads are empty. At the end of last week, in a phone call to a colleague in Germany, I was informed, that in the city where he lives the public movement in the center was reduced by 33 %.

WAIT, WAIT, WAIT, the private health care system seems to be very well equipped, and according to the latest news the government entered into agreement with private hospitals to provide ICU beds to everybody who needs. They showed also a statistic and with this agreement in place, Brazil comes close with 2.63 ICU beds/10k people to the number of ICU beds in Germany 3.04/10k people. They said, only São Paulo got more ICU beds than there are in entire France. However, my wife said "mentira" once she saw this.

Now back to the time series analysis, according to the numbers, we in Brazil need to keep this regime tight for another 3 weeks and then may start to loosen it in a sensible manner. With only a little bit of luck, this can be achieved before the start of winter time.
 
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obsigna

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I know this of course, and for this reason I wrote "That means, once a spread has been verified to have passed the turning point, we know with a probability approaching certainty how it ends up."

To be sure, that we passed the turning point, the curve fitting must be repeated when new data is available. ...
I just repeated the analysis for Germany and Italy with today's data, and both have clearly passed their turning points and the results are clearly converging, that means the differences in the limiting values as resulted by the day-to-day curve fittings are relatively small.

Italy: 112942 (today) - 115429 (yesterday)
Germany: 47664.1 (today) - 43857.6 (yesterday)

The time series for the U.S. is quite on track even if the turning point would be reached only tomorrow
150944 (today) - 144036 (yesterday)

The time series for Brazil is still quite erratic - it is simply too early, and the turning point cannot be clearly established. Here applies what ralphbsz said, that "Fitting a logistics curve depends crucially on finding the turning point" and so the previsions are very very uncertain, however, it seems that finally the number of cases will be very much lower than in Europe and in the U.S.
 

mark_j

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According to a study done here, we're looking at at best 3 months of so-called "social distancing" and self isolation:

All the pre-emptive measures in the world can't help us when stupidity rules:

One of our states was stupid enough to release 2700 people from a cruise ship of which 130 have tested positive while out and about in the general populous. At least I'm 800 kms from that mayhem...
 

rigoletto@

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WAIT, WAIT, WAIT, the private health care system seems to be very well equipped, and according to the latest news the government entered into agreement with private hospitals to provide ICU beds to everybody who needs. They showed also a statistic and with this agreement in place, Brazil comes close with 2.63 ICU beds/10k people to the number of ICU beds in Germany 3.04/10k people. They said, only São Paulo got more ICU beds than there are in entire France. However, my wife said "mentira" once she saw this.
I don't have any idea of how many ICU beds are available in the private sector but my father was in an ICU in Rio a few years ago, and they had about a hundred of beds in there, and that wasn't really one of those top private hospitals. Also, in Rio the 'Riocentro' (huge convention and event center) is already set to be converted in a field hospital if necessary.

We still have the military hospitals which are often well equipped, not crowd and the staff is well prepared.
 
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obsigna

obsigna

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I use numpy,pyplot & polyfit,polyval. It will take a week before I know if predictions are ok.
The model is some wet vinger work.
The code is so small I don't think I can reduce it using R or Julia

PS: Why would someone use C for predictive models ?
Why would somebody think that a polynomial is a model?

Why C? Well, I know it. I could have implemented the Levenberg-Marqwardt algorithm in FORTRAN (actually 30 years ago, I happened to use a FOTRAN curve-fitter on the command line). However, it would have never come to my mind to implement the LM algorithm and LU matrix decomposition in Python. Even JavaScript would be faster. That said, I could have simply used the GNU Octaves's (C++) leasqr() function for curve fitting, however, that would have left me anyway with the problem of data extraction.
 

Alain De Vos

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Every tool is good if it does the job.
But why is a logistic function better than another model ? Meaning choice of model can have big impact on prediction certainly farther in the future.
 
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obsigna

obsigna

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...
But why is a logistic function better than another model?
...
I have written in my initial post:
As a matter of fact it is THE MODEL for almost all natural growth processes, and it would be extremely surprising if not for the present spread of Covid-19 in given populations. I proved already, that the logistic function described very well the spread in China. So why not in other regions of the world as well.
Besides that I gave tons of links which would tell you everything you always wanted to know about the logistic function and were afraid to ask for.
 

Alain De Vos

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Well , the only time I saw a logistic function was when modeling a neuron.
And I did not say that the logistic function is not the best choice.
Bye the way, tanh has also a nice graph,
 
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obsigna

obsigna

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Well , the only time I saw a logistic function was when modeling a neuron.
And I did not say that the logistic function is not the best choice.
Yeah, electrochemical transport controlled (diffusion and migration limited) processes are 100 % matches for the logistic function. I am an electrochemist and the LF is well known in our field.

PS: Here comes the curve for Belgium with the data of today:

Belgium.png


We need to wait a few more days, to be sure, but it seems to be a quite good fit. It says the turning point was today, but because of the deviation of the cases data on the weekend, the fit of tomorrow might tell us otherwise.
Code:
Model: a/(1 + exp(-b·(x - c)))
       a =   8739.46 ± 6.5144 %
       b =  0.249949 ± 2.5576 %
       c =   63.1012 ± 0.76079 %
  ChiSqr =  1393.336
PPS:
Bye the way, tanh has also a nice graph,
The tanh function is out of question, because it crosses 0 in an 45° angle. We are looking for a function which starts at 0 with a gradient of 0 and then slowly grows up. The mere exponential function does this as well, however, this is out of question, because it quickly approaches to infinity, and besides it does not fit to the data as nicely as the logistic function does. Here again Belgium with an exponential curve fit:

Belgium.exp.png
 

Alain De Vos

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In Belgium there is a capacity of 2000 "high care" beds for Corona of which currently 200 are used.
 

ralphbsz

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You're correct, the public health care system of Brazil got by far not the ICU resources as for example the health care system in Germany. My guess is, that everybody (but a few infamous exceptions) in Brazil is aware of this and is sufficiently scared about this, and this is the reason why a vast majority of the people here does not question and supports the precautious measures.
I had the bad luck of spending several weeks doing daily visits to a patient in the ICU of a rural Brasilian hospital (my father). Both times he survived. The care in the ICU was excellent, the doctors well trained, hygiene good, nursing staff plentiful, helpful, and skilled. But in rural Brasil, the number of available ICU beds is low. As I said: Campo Grande has 14 at the Santa Casa (the SUS hospital), and at most another 10 or a dozen at the other three hospitals in town, for a city of 3/4 million people (which is also the supercenter for a state of 2.8 million people (I wrote 4 above, wrong). Of those, 1 (!) is an isolation bed in a separate room. That's WAY below european standards. I just saw in the news that the Uniklinik (university hospital) in Leipzig alone has 14 beds in the isolation ward of the ICU alone, and Leipzig is a medium-size town!

Where things fall apart in Brasil is in the non-intensive non-specialty part of the public health system. The regular parts of the government hospital there has serious problems with staffing, medication, supplies (even alcohol for disinfecting and toilet paper is chronically in short supply, we ended up bringing it). Nutrition for the patients is not good, and the expectation is that families station people in the hospital to be with the patient, to supplant the minimal nursing staff. Been there, done that. Not fun.

And if you go outside of cities, it gets REALLY dire. My parents used to live in a village of 2000 people, about an hour from the nearest city. There is a health post there, with one doctor from 9-5, and two nurses. And one ambulance, but half the time that ambulance is on the way to the city or back. It's better than nothing, but it is not good at all. If you then go to farms that are another hour away from little villages (and where a certain fraction of the rural population lives), health care is non-existing. Only serious cases get brought to cities, often only when they have reached very serious condition.

But then, you can't average rural brasil, not even a provincial capital, with Sao Paulo and Rio, which are big, somewhat wealthy, and international cities. With the wealth, they also have way more private health care, whereas in rural Brasil, the public system takes care of much more.

Let me tell you a little story about how good the Brasilian public health care system is. My dad has heart problems (and many others), and being part German, he got an artificial heart valve in Germany. But he got a hyper-modern one, which didn't require cutting him open like an oyster, but was inserted through the aorta. When he was in the ICU in Brasil, all the cardiologists at the hospital were amazed: they had heard that such things exist, but had never seen such a valve! They asked where he had it implanted, and my sister and me explained that it was the common standard of care for elderly patients in Germany. Then they said that there was only ONE hospital in Brasil that was able to implant those valves: the big SUS hospital in Sao Paulo (no, not the Albert Einstein or the Campinas University one, the public SUS one). We heard similar things from doctors (we spent a lot of time chatting with them) and folks in the elder-care industry (both my parents are in nursing care): the private health system in Brasil is medically decent, comfortable, and caters to the wishes of the middle and upper class. The public health system is unfomfortable, dirty, poor, and excellent. If you have something minor (uncomplicated baby delivery, broken arm), you go to the private medical system for luxury and comfort. If you have something seriously life threatening, you go to the SUS public system, or you fly abroad. Now, I don't know whether this applies also so much in Rio and Sao Paulo; my uncle in Sao Paulo swears by the Albert Einstein hospital, which is clearly very good and private.

WAIT, WAIT, WAIT, the private health care system seems to be very well equipped, and according to the latest news the government entered into agreement with private hospitals to provide ICU beds to everybody who needs. They showed also a statistic and with this agreement in place, Brazil comes close with 2.63 ICU beds/10k people to the number of ICU beds in Germany 3.04/10k people. They said, only São Paulo got more ICU beds than there are in entire France. However, my wife said "mentira" once she saw this.
Well, "mentira" (which means lies) may be a bit of an exaggeration. A lot depends on how you define "ICU". In Campo Grande, the moment you need a ventilator, you will be in the ICU, or else you will be dead if all 14 beds are occupied. I know that in Germany, they use ventilators in intermediate rooms (better equipped than regular rooms, but not ICU). So comparing the numbers isn't all that easy. So counting what is an ICU bed or not probably depends on local definitions.

Now back to the time series analysis, according to the numbers, we in Brazil need to keep this regime tight for another 3 weeks and then may start to loosen it in a sensible manner. With only a little bit of luck, this can be achieved before the start of winter time.
Next time you update, if you happen to have graphs for other countries, posting then would be appreciated.
 

Crivens

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That is why I like this place. Someone solves a problem he has, makes that public, and the sure-as-heck to come probing (otherwise known as bickering) of the methods is both civil and on a level most people out there won't get. Great.

W.r.t. Russia, my grapevine sings about them stamping almost all deaths of this bug as pneumonia. That may be technically correct.

One lesson learned from this is to check and heavily control the use of antibiotics in livestock management. The areas with high rates of people dying correlates with high-density animal farming. MRSA is a high cause factor here.
 
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