Covid19_Data.m_2.zip
total-cases-covid-19-who.xls
total-deaths-covid-19-who.xls

@Christopher2222 

Yeah, it's common to hear than Italy has more older people than other wseter Europe countries. But this seems infermed by the facts (it depends where the limit between elderly and not elderly is set).

Statistics about populations (age distribution in particular) can be found gere (in french):
http://perspective.usherbrooke.ca/bilan/servlet/BMPagePyramide?codePays=ITA&annee=2018

Here is an excerpt for Italy and France
France_Italy.xls    France_Italy.ppt

I prefer considering french and italian populations are quite comparable and search elsewhere for an explanation of the difference between the number of deaths in the two countries:

• It's commonly said that France and Italy have the same evolution excepted that France's is delayed by about 7 to 8 days.
  This seems to be confirmed by the curves but persumes nothing about the future. At the early stages of this outbreak all the curves loog rougly the same.
   
• The italian health system, especially the health care system for the elderly, is trongly different from the french one. In France there are a lot of dedicated structures named EPHAD (a kind of small public clinics for dependent adults) and in private structures. They all gathered 728000 persons by the end of 2015
  (https://drees.solidarites-sante.gouv.fr/IMG/pdf/er1015.pdf, in french)
  Nothinq comparable in Italy where 380000 "badanti" (kinds of life support workers) assist older people at home. And this, I belive, is potentially a major source of contamination and probably the better explanation to the huge number of deaths Italy counts.
   

One says that France and Italy have the same evolution excepted that France's is delayed by about 7 to 8 days.
Based on the hypothesis of roughly equivalent distributions of the elderly, one can predict about 1500 deaths by the end of the next week. In 7-8 days we will have an idea of the benefit of one healtf system over the other, if benefir there is...


Understanding crowd dynamics is pretty chaotic when driven by fear: I went this morning to the bakery and it was practically empy at 11 am, the waitress said me one man came and bought 80 "baguettes" (about 20 Kg of bread) to freeze it in case of... 
In France all the supermarkets are assaulted by people stocking foods just as it probably happened 80 years ago when WW2 was declared. And all this crowd packed in front of the gates waiting for them to open do not even realise that this is the best way to spread the virus!


PS : here is a bar graph which give for each EU country the percentage of people at least 60.
Germany is equivalent to Italy regarding to this criteria, but at the same time counts 9 deaths for 5100 confirmed cases. 
I think that discipline and adherence to recommendations is the main explanation to this extremely low death rate (yesterday evening the french prime minister publicly said he was appalled at laxity of its fellowed citizens and ordered strong confinement actions). The Latin temperament is well known for its laxity and for its bravado and anti-establishment side: Italy probably pays for that and France will probably pay too.

@Christopher2222 

The great statistician George Box once said "All models are wrong... but some are useful". I do hope yours are wrong :-)
Right now the only reliable feedback we  have about this outbreak seems to be found to the side of far east countries (China, South Korea, Japan, ...). For all of them the peak is behind them (if no rebound is going to happen) and this gives information about the length of the exponential growth phase.
Values of the mortality rate can also be infered and even a possible variation due to containment policies, health care policies, ageing of the populations and so on. This "far east" mortality rate seems to range from 2% to 4% with a mean (strongly conditionned by the Wuhan region) around 3%.

In western Europe Italy takes the lead (nothing funny here) with a mortality rate around 7% and there is no good reason to think that France or Spain will not raise to levels this high (or at least 5%, if one optimistically consider Italy is the Wuhan of western Europe and France its South Korea).
Germany is strangely appart with an extremely low 8/4500 apparent mortality rate.
This notion of apparent mortality rate is extremely important for anybody can do this simple operation to divide a total number of deaths by a total number of confirmed cases. But problems arise when "authorized" people taking the seasonal flu as an example say that "given 2 person out of 3 are healthy carriers, the true rate mortality is around 1%".
More of this it is very simple math to prove that this apparent mortality rate is generally an underestimate of the true mortality rate :

• Let C(t) the evolution of the cumulated number of confirmed cases over time t. From its definition C(t) is a non decreasing function of t.
• Let r the true mortality rate, supposed constant over time, and T the time between the detection of the infection and the death (if it fhas to occur).
• Then the  apparent mortality rate defined as r*C(t-T) / C(t) is necessarily smaller than r.

In practice T is not a constant but can be identified to a random variable with support  [a, b] (a > 0), and it may happen that the apparent mortality rate exceeds the true mortality rate at some times t. But it is more reasonable to think that the true mortality rate is larger than the apparent one.

I think Bayesian inference could help to assess the (posterior) distribution of this true mortality rate given adhoc priors and credible working hypotheses. The main issue here is that the populations of the dead ones is not given with enough details (in particular the distribution of the number of days from detection and death is unknown... which means it becomes a nuisance parameter which is needed to infer jointly with the true mortality rate).


This is not doing politics to say that, even if all the western countries are globally in the same situation (or will be due to date lags), the official discourses radically differ. In democratic countries I like to believe these discourses are based upon scientific opinions... which is even more creepy because this means scientific do not agree at all. Think to Germany and the UK saying thant 70% to 80% of their citizens will be affected whilen, at the same moment, France expects the peak of the outbreak to the end of the next week (leading to a 17000 confirmed cases estimation).

China has been mocked for the extreme measures she has taken, but this resulted in about 56 confirmed cases per milions of inhabitants. 15000 kms far from there Italy now lives with about 300 cases out of a million. Does this difference come from the early containment policy China applied or from the more and more common claims about a second strain more agressive than the China's one?

I regret that a so small number of informations are avaliable because this reduce any attempt to run a detailed analysis to pure speculation. The only thing I'm capable to do right now is to compare growth curves and to imagine the reasons of their discrepancies. Where does a mortality rate of 7% in Italy come from? From this second more lethal strain ? Or from the testing strategy (if a country tests only people that already present accute symptoms, it's likely to think that a large amount ogf them will die). But this last hypothesis seems to be infirmed by comparing the number of tests Italy, France and South Korea did and comparing their respective growth curves of confirmed cases.

If CoVid19 passes its way without paying to much attention to me  I plane to update this post with newer results.

Thanks for your attention.

@acer 

Thanks for your return, I'm going to look at these links right now

@Carl Love 

Thanks Carl, It works perfectly well

@Carl Love @tomleslie

It's Maple internal format file indeed, I would have mentioned it.

Hi often meet the same problem (Windows 7).
When this issue happens, the only solution is to kill the task from the task manager.
I never faced this kind of problems with Maple 2018, 2016, 18, 15.

Other problems :

1. If I keep open a session for many hours (typically a lengthy code that runs a part of the night), the session is freezed: no possibility to save worksheets, iconify the maon window nor even kill it by clicking on the upper right ren icon.
2. As soon as the number of windows in a same session exceeds 4, 5 or 6, any attempt to open a new one results in a "connection to the kernel lost" popup message
3. Idem point 2 if an even smaller of windows in open for a longer time (let's say a few hours).
   Note that the problem seems to happen even if Maple uses a small amount of the memory (I have 64 Gb and I can face these issues as soon as Maple uses a few hundreds of Mb)

Note I always work in worsheet mode with the "old" malple input style.

I use a floating licence of Maple 2019 (as for older versions).

This forced me to rediscovered the old "write a few lines and save the file" practice

@acer 

You're right: without any mention of the method to use evalf+Int returns a correct value.

The very reason I explicitely used the option "method" is because Maple failed to return a value for more complicated functions.

Among the different values of "method" a few method of them succeeded to return a correct approximation, while some others only gave the unevaluated integral (which is quite understandable).

So I tried to identify a "robust" method for the class of problems I was concerned of.

This is while I was unsuccesfully doing this that I came to simplify excessively my integrands of interest and discovered that "surprising weakness".


Thanks for the advice about the help pages
 

@Carl Love 

Hi,
Where can I find information about "initialization files", in particular what they may contain and how to read them each time I log in?
For instance, I often have to load the same set of packages, to do plots with gridlines set to true and a specific titlefont...

Thanks in advance
 

@Carl Love 

Thank you Carl for the precision

@Joe Riel 

Great, I didn't know about this syntax and I vote up.

I use tio use MathML to define this kind of variables ... but is its a little bit abstruse :
`#mrow(msub(mi(f),mrow(mi("α"),mo(","),mi("β"))))`

A shame that the help page concerning the neutral & doesn't give an example like yours.

@Kitonum 

What led me this reply was the PO saying "I want to use non-linear least squares fitting to minimize the error between two curves", not between values of f1at some points and the the values of f2 at the same points.
It happens the the method I proposed performs well on the example I used (thanks to you to have chosen a range 0..5 or 0..2 I reused for myself)

Note that the method I used is not guaranteed to return a solution: for instance, fsolve fails to return a solution when the lower bound of the integral goes to (-3/5)⁺ (I did not try NonLinearFit in this situation).

Last point which has nothing to do withe the "fitting" method we use : it's not possible to have a "visually" good fit if the upper bound of the integral in my approach, or the value of b in yours, is less than -3/5.
This can be easily understood by comparing the derivatives of f1 and f2 with respect to x.
Thus, in a certain sense, the initial problem is not posed in a sufficiently clear way.

@Carl Love 

Of course, the 3d error is included as a screen capture at the end of the attached file.
But here it is again

It is not the usual pink font of MAPLE errors: I did some search on the wed and I found a MapleSoft page where an explanation of the error and the way to fix it is given.
But I didn't try to do it for the reason that I get no problems at all if I use "classical" modification of the tickmarks. I think this error is related to the use of MathML in tickmarks.

A last point: sometimes the plot3d command doesn't return an error but more often than not it does.

Oh, I almost forgot: your code doesn't produce any error

@acer 

Thank you acer.

@Kitonum 

Apologies: I didn't payed attention you simply wrote r=1..3 instead of parameters=[[r=1..3]].
So you're right, r=1..3 doen't work with MAPLE 2015.2