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Paul
Posts: 10791
Joined: July 20th, 2001, 3:28 pm

### Re: Models for Covid-19

This is a very good source of data for the UK: https://www.england.nhs.uk/statistics/statistical-work-areas/covid-19-daily-deaths/

Looks like age distribution of deaths is not much different from that for flu. Of those that died flu might actually start younger.

Cuchulainn
Topic Author
Posts: 62626
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Models for Covid-19

Euler's method for SIR
https://www.maa.org/press/periodicals/l ... or-systems

Why not?

When will it end? Per country,

https://ddi.sutd.edu.sg/

+ csv data
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

Paul
Posts: 10791
Joined: July 20th, 2001, 3:28 pm

### Re: Models for Covid-19

It would be nice to see the values for the two SIR parameters in each country. And then an explanation of why they are different from country to country. Otherwise it could just be a curve-fitting exercise, for which any S-shaped (totals) curve would do!

The Russian numbers are interesting. Clearly they are reporting numbers according to what the model says, rather than what they are actually seeing!

Paul
Posts: 10791
Joined: July 20th, 2001, 3:28 pm

### Re: Models for Covid-19

There are two parameters in the SIR odes. But there are also initial conditions, for initial number of infected (that's easy) and initial number of susceptibles (that's the interesting bit).

Their plots are very symmetrical which (I think) corresponds to a small removal rate of infectives. If that's the case then total infectives will asymptote to the entire 'population' i.e. the initial number of susceptibles. Which is the interesting thing because that is what might determine whether there will be second waves.

I want to see their parameters and initial conditions!

Paul
Posts: 10791
Joined: July 20th, 2001, 3:28 pm

### Re: Models for Covid-19

Take Italy. (No, seriously, take it.) The decay to the right of the peak is much slower than the growth. It's similar for many countries. You can get that with SIR (I think), so I'm worried about their parameters.

katastrofa
Posts: 9455
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Models for Covid-19

What does and epidemiological microsimulation look like when it's at home?
Is it defined or just a buzz-word?

It would seem that the lack of support for demographics (McKendrick model?) in the Swedes' models caught them on the hop.
It's an individual-based simulation of the contagion spread - from person to person. The point is that the persons and their interactions vary.

Cuchulainn
Topic Author
Posts: 62626
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
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### Re: Models for Covid-19

Should ye all not be examining these ODEs as dynamical systems to give richer results such as equilibria and asymptotic stability, e.g. when

$\frac {\partial r}{\partial t} = \frac {\partial i}{\partial t} = \frac {\partial s}{\partial t} = 0$.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

Paul
Posts: 10791
Joined: July 20th, 2001, 3:28 pm

### Re: Models for Covid-19

Improved estimates for number of population infected making some allowance for age (of population not my age, although that might become relevant):

Lower   Upper

Belgium         17.0%   32.8%
Spain             13.8%   26.5%
Italy                10.9%   21.0%
France             9.7%   18.7%
Netherlands     9.7%   18.6%
Ireland             8.9%   17.1%
UK                   8.5%   16.3%
Sweden           6.4%   12.4%
USA                 5.7%   10.9%
Switzerland      5.2%   10.0%
Luxembourg    4.8%     9.3%

(I'm keeping one decimal place because it's looks cleverer. The accuracy does not justify it though!)

jimjust
Posts: 1
Joined: November 25th, 2008, 7:04 pm

### Re: Models for Covid-19

At the Imperial College site, look for Report #13.  There will be a link to download the code:
Replication code for "Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries"
Here is the direct link to the download in either zip or tar format:
https://github.com/ImperialCollegeLondo ... s/tag/v1.0

Cuchulainn
Topic Author
Posts: 62626
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Models for Covid-19

Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

Cuchulainn
Topic Author
Posts: 62626
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Models for Covid-19

At the Imperial College site, look for Report #13.  There will be a link to download the code:
Replication code for "Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries"
Here is the direct link to the download in either zip or tar format:
https://github.com/ImperialCollegeLondo ... s/tag/v1.0
Don't suppose you'd care to walk us through/explain the code?
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

katastrofa
Posts: 9455
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

### Re: Models for Covid-19

I thought this is the model they used for the UK - ?
https://github.com/mrc-ide/covid-sim

Paul
Posts: 10791
Joined: July 20th, 2001, 3:28 pm

### Re: Models for Covid-19

Euler's method for SIR
https://www.maa.org/press/periodicals/l ... or-systems

Why not?

When will it end? Per country,

https://ddi.sutd.edu.sg/

+ csv data
Here is their current plot for the UK:

I've checked their results. And it confirms what I was worried about.

I got the data from https://datahub.io/core/covid-19#resource-time-series-19-covid-combined.

I tried fitting a classic SIR model, solved via simple Euler. However I didn't trust my numerics. With a small removal rate of infectives which is what I suspected they had found for most countries (because of the symmetry in their plots) there is a simple formula for infectives. So I fitted that and got the following:

Very similar.

However, the SIR model has two parameters in the odes, and two initial conditions. As I said, I had one parameter being zero. One initial condition, for number of infected, was easy. I started at I=85. That leaves just the infection rate and initial number of susceptibles, S_0, for fitting.

The best fit had S_0=140,000. That's what I was worried about.

What they have done, it seems, is fit a perfectly decent model to an uncontrolled infection in a rather sparsely populated island. That is not the same as what we have, an infection in an island with a large population with lockdown.

At the moment it looks like something I said weeks ago: All models give the same shape curve. Which is the right one? Why not just fit any S-shaped curve (to totals), and not worry about justifying the model?

If their results turn out to be correct then I think it's more luck than anything. For zero removal rate the solution of the odes is the logistic function. Which is probably the function you'd choose for fitting in the absence of a model anyway!!!

Cuch, if you're feeling strong you could repeat this with non-zero removal rate. As I also said, the data suggests for many countries that it is non zero because of the slower decay after the peak, than the growth before. (I.e. asymmetry.)

Cuchulainn
Topic Author
Posts: 62626
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

### Re: Models for Covid-19

Saw this priceless gem by chance

Warnings: (1) The basic reproduction ratio and the recovered persons use unfortunately the same capital letter R as symbol but one has to be aware that these are different entities. (2) Not all combinations of infection and removal rates within the ranges of the interactive model below will match a real existing infectious disease.
Step over the gap, not into it. Watch the space between platform and train.
http://www.datasimfinancial.com
http://www.datasim.nl

Paul
Posts: 10791
Joined: July 20th, 2001, 3:28 pm

### Re: Models for Covid-19

The Singapore model is being quoted in the media now. Would be nice to see confirmation of their analysis, e.g. for UK.

You can get the same sort of plot as they get if you scale everything up (infected, susceptibles, parameters) and assume that the vast number of people are asymptomatic or not bothering reporting the illness. But I'm still getting that the best fit has currently more infected than the initial population of susceptibles! I.e. fails the most basic sanity clause check. Yes, Cuch, there's no sanity clause!
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