Models for Covid-19

bearish · May 13th, 2020, 3:31 pm

Not to defend anybody in particular here, but would a carefully planned and executed 2-year software development project be of the slightest use in this context?

“We don’t know what to tell people yet; still working on part 2c of the requirements analysis...”

Paul · May 13th, 2020, 3:58 pm

Looks as if it's under control in Sverge.

I don’t think you can say whether that’s bad for Sweden, or good, until we know about second waves, collateral deaths, and even whether the numbers are correct. Not to mention cures and vaccines.

Cuchulainn · May 13th, 2020, 4:34 pm

Not to defend anybody in particular here, but would a carefully planned and executed 2-year software development project be of the slightest use in this context?

“We don’t know what to tell people yet; still working on part 2c of the requirements analysis...”

Out on the street, I was talking to a man
He said, there's so much of this life of mine that I don't understand
You shouldn't worry, I said, that ain't no crime
'Cause if you get it wrong, you'll get it right next time, next time

You need direction, yeah, you need a name
When you're standing in the crossroads every highway looks the same
After a while, you can recognize the signs
So if you get it wrong you'll get it right next time, next time

Life is a liar, yeah, life is a cheat
It'll lead you on and pull the ground from underneath your feet
No use complaining, don't you worry, don't you whine
'Cause if you get it wrong, you'll get it right next time, next time

You got to grow, you got to learn by your mistakes
You got to die a little every day just to try to stay awake
When you believe there's no mountain you can climb
And if you get it wrong, you'll get it right next time, next time
Next time, hmm

The answer:all that money slushing around and the best they can do is simple ODEs and logistic functions.
It's not rocket science (even I solved those ODEs in < 1 days) but the whole debacle is a SHAMBLES.

Paul · May 13th, 2020, 4:43 pm

I have no idea what happened between all the SIR talk and the latest code. Is all a mystery.

But I read that there are 450 parameters in the latest model, none of which will be known.

As for R_0, I think of it as an output, like implied volatility. Vol comes about by trading. We get a handle on it by looking at implied vol. It levels the playing field. That's what R_0 does. You can compare through time and across countries.

Cuchulainn · May 13th, 2020, 8:22 pm

I have no idea what happened between all the SIR talk and the latest code. Is all a mystery.

But I read that there are 450 parameters in the latest model, none of which will be known.

As for R_0, I think of it as an output, like implied volatility. Vol comes about by trading. We get a handle on it by looking at implied vol. It levels the playing field. That's what R_0 does. You can compare through time and across countries.

I have read this is the last version

https://github.com/mrc-ide/covid-sim

and that will be my report.

There could be more versions and since the project seems to be chaotic multiple versions will be spawned.

Paul · May 15th, 2020, 1:20 am

Manchester Uni say 19 million Brits have had it. I estimate 21 million. So they are very close.

Cuchulainn · May 15th, 2020, 9:14 am

Logistic function better. Or an asymmetrical version of it.
Why? Better at what?
Nothing special about this function, meiner meinung nach.
The logistic function comes out of many math biol models (as well as other fields), including some epid. models. Or it's at least a decent approximation to what comes out of these models. So it's not unreasonable to fit that function. By "asymmetrical" I just mean that the basic logistic function doesn't capture the asymmetry in the growth and decay phrases of an epidemic. Hence needing a slightly more general function for fitting.

But taking an arbitrary function and fitting it seems a bit silly. It's usually nice to have some plausible excuse for a functional form!

I don't know what the "cubic" model does. But cubics do go off to plus/minus infinity, so I hope it's not modelling deaths!

I've been thinking about this and I agree. From an approximation theory viewpoint cubic polynomials are untrustworthy (many reasons) but as Paul says they are uncoupled from any underlying model. All they do is create pleasing-to-the-eye smooth curves. See any undergrad book on numerical methods.
(Verhulst) logistic function on the other hand is based indeed on models that crop all up over the place. They correspond to simplifications in SIR models etc.
I tried to find models from the confident Swedes. i could only find this 'note' (not peer-reviewed I am sure, the authors even don't believe what they are writing .. section V).

https://arxiv.org/abs/2004.01575

Thy reduce the ODEs to Woods-Saxon forrn (nuclear physics analogy...). This confounds the material and is non-standard .. just use/learn the Verhulst model and it's a starting point, indeed. Why drag physics analogies into the discussion??

// This 3-page, 4-author note has several typos, is incomplete and unresearched if you look at the references.
Very unconvincing.

Cuchulainn · May 15th, 2020, 10:38 am

Manchester Uni say 19 million Brits have had it. I estimate 21 million. So they are very close.

I almost read Man United!

bearish · May 15th, 2020, 1:46 pm

Manchester Uni say 19 million Brits have had it. I estimate 21 million. So they are very close.
I almost read Man United!

Me too. A Solskjær effect, probably.

Cuchulainn · May 15th, 2020, 2:06 pm

Another cunning stunt!

Cuchulainn · May 16th, 2020, 8:50 pm

Any more models? Still, SIR ODEs are almost linear...

What about predator-prey?

Paul · May 16th, 2020, 9:24 pm

They're the same.

Cuchulainn · May 17th, 2020, 7:42 am

They're the same.

But the discussions/articles on SIR models seem to be more superficial (they all end up with a curve.)

They only tackle a subset of the use cases. A lot is quite sterile and lacking in something that I can't quite put my finger on.

Have phase portraits fallen out of favour?

It ain't what you do it's the way that you do it 

And that's what gets results

Paul · May 17th, 2020, 7:33 pm

Not unrelated:

I've started to read (sorry haven't saved any refs) that R_0 isn't necessarily the greatest thing since sliced bread (no kidding!), and even that R_0 going above one might not matter, something about variability in R_0 makes things safer.

I am confused.

If you have a simple exponential growth (early stage of epidemic) with a growth rate which varies across populations, say, then the average number of infected is not given by the number of infected using an average growth rate. In fact it's worse. It's simple Jensen's Inequality.

There's probably a Certainty Equivalent Rate of Infection you could calculate.

Cuchulainn · May 17th, 2020, 7:50 pm

Fifty shades of [$]R_0[$]?

Just imagine 50 shades of Navier-Stokes. No planes would leave the ground.

A search from my armchairs threw up this

https://pdfs.semanticscholar.org/a8d1/8 ... f2e6fb.pdf

No idea what it does but some buzzwords might be right.

//
is prey == h = healthy, predator == I?

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