Paul,

How many houses in the system of ODEs? [$]H_i, i = 1,...N[$]

What's [$]N[$]?

- Cuchulainn
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Paul,

How many houses in the system of ODEs? [$]H_i, i = 1,...N[$]

What's [$]N[$]?

How many houses in the system of ODEs? [$]H_i, i = 1,...N[$]

What's [$]N[$]?

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http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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- Cuchulainn
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Or thisI'll probably start a separate thread for modelling issues as opposed to numerical. Meanwhile this is the world we live in now.

2020-03-24_110017 - Model 1.jpg

http://www.datasimfinancial.com

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

I had ten. You can have as many as you like! You'll have to adjust the parameters though, specifically [$]\beta[$]. I should really non dimensionalize I guess!Paul,

How many houses in the system of ODEs? [$]H_i, i = 1,...N[$]

What's [$]N[$]?

I haven't yet figured out how to best aggregate/homogenise the many households.

kat, I think what is interesting about the simple model is how it shows that lockdown has to be early, before households have an infected member. Any ideas about how to estimate numbers? IC vs Oxford.

- Cuchulainn
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For N = 100, this will be a system of 400 equations.I had ten. You can have as many as you like! You'll have to adjust the parameters though, specifically [$]\beta[$]. I should really non dimensionalize I guess!Paul,

How many houses in the system of ODEs? [$]H_i, i = 1,...N[$]

What's [$]N[$]?

I haven't yet figured out how to best aggregate/homogenise the many households.

http://www.datasimfinancial.com

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

- Cuchulainn
**Posts:**61609**Joined:****Location:**Amsterdam-
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That would never catch on. That's why they should have done proper testing up front.kat, I think what is interesting about the simple model is how it shows thatlockdown has to be early, before households have an infected member. Any ideas about how to estimate numbers? IC vs Oxford.

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

Jean Piaget

- Cuchulainn
**Posts:**61609**Joined:****Location:**Amsterdam-
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Not really. It's which model is best. There are many institutes working on this.IC vs Oxford.

Curiosly, neither IC nor Oxford have published the gory details. Until we see, it's all a bit of hot air at the moment.

What about Matt Keeling at Warwick?

https://homepages.warwick.ac.uk/~masfz/ModelingInfectiousDiseases/Chapter3/Program_3.4/index.html

http://www.datasim.nl

Every Time We Teach a Child Something, We Keep Him from Inventing It Himself

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- katastrofa
**Posts:**8982**Joined:****Location:**Alpha Centauri

No such a thing as proper testing. The antibody test the gov buys has very low sensitivity and specificity (high number of false positives and negatives), afaik.That would never catch on. That's why they should have done proper testing up front.kat, I think what is interesting about the simple model is how it shows thatlockdown has to be early, before households have an infected member. Any ideas about how to estimate numbers? IC vs Oxford.

That's misleading. You can ignore the [$]R_i[$]. And for deaths you only need [$]H[$] not [$]H_i[$]. So it's technically 201.For N = 100, this will be a system of 400 equations.I had ten. You can have as many as you like! You'll have to adjust the parameters though, specifically [$]\beta[$]. I should really non dimensionalize I guess!Paul,

How many houses in the system of ODEs? [$]H_i, i = 1,...N[$]

What's [$]N[$]?

I haven't yet figured out how to best aggregate/homogenise the many households.

But that's also misleading. 100 are identical, just different initial conditions. Ditto another 100. Not even different parameters! All that really matters is how these are averaged/aggregated, and it's not immediately obvious how to do it analytically.

If it was really 400 or even 201 I'd be the first to complain! I even complained about seven!

Cuch, could you try it for ten, 100, etc. households and you'll see little change to results (as long as you scale parameters correctly).

I mean IC or OxfordNot really. It's which model is best. There are many institutes working on this.IC vs Oxford.

Curiosly, neither IC nor Oxford have published the gory details. Until we see, it's all a bit of hot air at the moment.

What about Matt Keeling at Warwick?

https://homepages.warwick.ac.uk/~masfz/ModelingInfectiousDiseases/Chapter3/Program_3.4/index.html

Oxford has many more already infected than IC (I think).

The wordometers numbers underestimate infected, obvs.

My best guess is 250,000 in UK infected currently.

- katastrofa
**Posts:**8982**Joined:****Location:**Alpha Centauri

"Any ideas about how to estimate numbers?"

You could fit the model to the trends.

You could fit the model to the trends.

Easy to solve for [$]I_i[$] in terms of [$]S_i[$]. Something like (not checked)

[$]\frac{d^2 (\ln S_i)}{dt^2}+\lambda \frac{d (\ln S_i)}{dt}=(\alpha-\beta)\frac{dS_i}{dt}-\beta \frac{d\sum S_j}{dt}[$]

Sum is over all households, inc. [$]i[$].

[$]\lambda=\gamma+\delta[$]

Prob not the best way to write it.

And I'll have to figure out initial condition for [$]\frac{dS_i}{dt}[$].

[$]\frac{d^2 (\ln S_i)}{dt^2}+\lambda \frac{d (\ln S_i)}{dt}=(\alpha-\beta)\frac{dS_i}{dt}-\beta \frac{d\sum S_j}{dt}[$]

Sum is over all households, inc. [$]i[$].

[$]\lambda=\gamma+\delta[$]

Prob not the best way to write it.

And I'll have to figure out initial condition for [$]\frac{dS_i}{dt}[$].

- katastrofa
**Posts:**8982**Joined:****Location:**Alpha Centauri

Why not run it through Mathematica? Alan?

Kat, could you check the above?! I'm going around in circles. (I'm getting different things for the simple [$]\alpha=\beta[$] case depending on whether I sum over [$]i[$] before or after solving for [$]I_i[$]!)Easy to solve for [$]I_i[$] in terms of [$]S_i[$]. Something like (not checked)

[$]\frac{d^2 (\ln S_i)}{dt^2}+\lambda \frac{d (\ln S_i)}{dt}=(\alpha-\beta)\frac{dS_i}{dt}-\beta \frac{d\sum S_j}{dt}[$]

Sum is over all households, inc. [$]i[$].

[$]\lambda=\gamma+\delta[$]

Prob not the best way to write it.

And I'll have to figure out initial condition for [$]\frac{dS_i}{dt}[$].

Easiest to write

[$]\sum_{j\ne i}I_j =I-I_i[$]

to see what is going on.

Ok, integrated once, errors possibly corrected and with initial conditions included we are left with

[$]\frac{S_i'}{S_i}+\lambda \ln S_i -(\alpha -\beta) S_i-\beta S = c_i[$]

where

[$]c_i=\lambda \ln S_i(0) -(\alpha - \beta) I_i(0) -\beta I(0)-(\alpha-\beta) S_i(0)-\beta S(0)[$],

[$]S=\sum_j S_j[$],

[$]I=\sum_j I_j[$],

and

[$]\lambda=\gamma+\delta[$]

Will need initial condition [$]S_i(0)[$] and [$]I_i(0)[$].

[$]\frac{S_i'}{S_i}+\lambda \ln S_i -(\alpha -\beta) S_i-\beta S = c_i[$]

where

[$]c_i=\lambda \ln S_i(0) -(\alpha - \beta) I_i(0) -\beta I(0)-(\alpha-\beta) S_i(0)-\beta S(0)[$],

[$]S=\sum_j S_j[$],

[$]I=\sum_j I_j[$],

and

[$]\lambda=\gamma+\delta[$]

Will need initial condition [$]S_i(0)[$] and [$]I_i(0)[$].

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