Flatten the Curve

@joe-shmo

Bold font was quoting you, the part of your post to which I was responding.

If you are looking at a logistical curve, g (x), then its derivative is [1-g (x)]*g (x).

Thought it was interesting in the context of the discussion so shared it.

So I tried to get a functional form of what I'm calling f(t) - the US death rate per 10^5 inhabitants. ( Figure 7: https://www.imperial.ac.uk/media/imperial-college/medicine/sph/ide/gida-fellowships/Imperial-College-COVID19-NPI-modelling-16-03-2020.pdf )

Unfortunately, no trendline in excel was a good fit for the data. Just to be clear, in order to get the data I clipped the image, imported into CAD software, and scaled the image appropriately such that I could trace the curve and directly measure the bounded area.

Using the decreasing Population Model:

P_o = Current Population ( https://www.census.gov/popclock/ )

x = 1/10^5 * Int { f(t) } dt ( from March 20 to October 20 )

x = 1/10^5 * 673.672

D( Oct 20) = 329, 443, 000*( 1 - e^( -x ) )

D ( Oct 20 ) = 2,212,000 Deaths

Paper Estimates 2,200,000 Deaths

% Error = 0.5%

So it has some issues, but it should be reasonable once we get into the thick of it.

If I Integrate up to the 27th ( the curve is pretty flat in this region - so it could be a crap prediction ) the number of deaths:

Unmitigated: 2200
Currently: 1701

I'll check again next week.

A good quantitative follow up "on flattening the curve" from 3 Blue 1 Brown. It is simulating an epidemic and analyzing the effects of various countermeasures (and their scope) we are employing like quarantine, social distancing, hygiene, etc... Hope you enjoy the video!

YouTube : Simulating an Epidemic

I wanted to bring this up.

Using the constant population Model

D = k*P*int[ f(t) dt ]

Where
P = Initial Population
k = 1/10^5 ( factor for per 100000 scaling)
D = total Deaths = 2.2 Million

I can do ( an admitted crude graphical integration ) I've clipped the image, imported it into CAD software. I scale the axis such that I can integrate directly by measurement.

To solve for the initial population:

2.2*10^6 = k*P*int[ f(t) dt ] from March 1 to Sept 30

int[ f(t) dt ] = 671.116

P = 3.278 *10^8

Ok, so that lines up pretty reasonably with the population of the US.

So if I do that integral up to today Mar 1 to April 18

D = k *P *int[ f(t) dt ] = 12,272

Does anyone remember this was supposed to be the unmitigated response?
We are mitigating and we are at substantially higher numbers ( 3 times higher ), our peak has been reached, ect..

from where I'm sitting practically nothing adds up with the London College paper. What gives?

This whole death toll thing has been a total joke. Check out April 14th, over 6 thousand deaths on that day.

Anyone believe that?

Good thing is, even after throwing in all the might have been covid, the totals seem to be coming back down to what they were earlier.

The death stats are purely propaganda.

I'm not sure if up is down or left is right anymore?

1)The peak of the London College Unmitigated response was due to be June. A any mitigated response should peak well beyond June ( down and to the right) .

2) One might think, well, we mitigated so hard we literally shut it down in its tracks. So we pushed the peak to the hard left, I would say that's possible... But, again, that peak should be much lower than the unmitigated response at this time.

On Day 48 (Today), the London College is just climbing to f(48) ≈ 0.415 Deaths per 10^5

Even if we round the population up to 3.30*10^8

Death Rate = k*P*f(48) = 0.415/10^5*3.30*10^8 = 1353 Death per Day

We were hitting comparable numbers 2 weeks ago. Either way you cut it, the predictions aren't making sense.

@joe-shmo

That model was designed to create hype, it did its job.

@Eladar
Says Eladar the irrelevant.

@joe-shmo said
I'm not sure if up is down or left is right anymore?

1)The peak of the London College Unmitigated response was due to be June. A any mitigated response should peak well beyond June ( down and to the right) .

2) One might think, well, we mitigated so hard we literally shut it down in its tracks. So we pushed the peak to the hard left, I would say that's possible... B ...[text shortened]... hitting comparable numbers 2 weeks ago. Either way you cut it, the predictions aren't making sense.

The Chief Medical Officer in the UK, Professor Chris Whitty, is saying that the basic reproduction rate is currently under 1 in the UK. This should mean that the number of new cases drops to single figures within a month or so. It should significantly affect the shape of the curve.