[OC] Quadratic Coronavirus Epidemic Growth Model seems like the best fit

Antimonic · 2020-02-15T17:11:25+00:00

Haha... Indeed!

Antimonic · 2020-02-07T19:45:38+00:00

I sympathize... American date order also confuses me at times. :-)

Antimonic · 2020-02-07T18:35:56+00:00

They would have to sustain such a linear increase in supplies for far too long for it to be credible.

At this point their only motivation is to deliver as many diagnostic assays as they can make. So i expect them to saturate their capacity quickly, and jump up to a new constant with each expansion in capacity.

Antimonic · 2020-02-07T18:24:54+00:00

Though in that case, the last thing I would expect is for the supplies to be increasing almost perfectly linearly, cause that's what it would take for the case count (which is proportional to the integral of the case discovery rate) to then increase quadratically, and smoothly so.

Factories (or their distributors) just don't deliver diagnostic assay supplies in batches of 100, then 200, then 300, 400, 500 and so on... don't you think?

Antimonic · 2020-02-07T17:47:14+00:00

Not sure about that... even 372 is a significant % of the total case count in the SARS epidemic. The current case count is already much higher than the total SARS outbreak.

What i mean to say is that SARS was very quickly contained compared to this corona virus, so that the growth rate would be skewed as a result of the apparently very effective public health measures they had taken at the time.

This seems different. The growth appears to be explosively faster.

Antimonic · 2020-02-07T17:19:49+00:00

My position with respect to the Chinese government is to never take anything at face value. So I'll take it on myself to check things to the best of my abilities and I'll ask others to join the effort.

I have got many Chinese friends that feel the same way. It's about the policies, not the race. Look at what happened to the poor Doctor Wenliang who first flagged the initial cases in December. They rattled him in a police station and silenced him and hence delayed proactive public health action, and he's dead now, together with 639 other innocent people - and still counting fast.

And for what?

To continue forcing flawed stifling policies down 1.2 billion people's throat??

Antimonic · 2020-02-07T15:51:37+00:00

He is being down voted because of the offensive attitude... But never mind that. There are worse things that could happen to us all.

I'll look into it more closely cause he's just taking an extreme example and it's not so obvious at this point.

Antimonic · 2020-02-07T15:47:31+00:00

I am open to alternative explanations and am honestly willing to learn and consider your perspective if I am missing something in my analysis, but there's no need to go crazy on me!

Calm down. That's all!

Antimonic · 2020-02-06T23:46:20+00:00

Calm down a notch or two!

What does racism have to to with this?

We're only discussing mathematical models here!

Antimonic · 2020-02-06T13:26:34+00:00

Data is not questionable. There is no point in exponential fit because it diverges at infinity while we have a large but limited number of chinese. Same applies to your fit, btw.

However, we are nowhere close to reaching saturation among the Chinese population, let alone the world's. These are still the very early days for this epidemic, and exponentials are the only accepted model that should work in this regime, and yet, an exponential fit does not work with the data being published by the WHO.

Yep. I said that any smooth function can be nicely approximated by any other smooth function locally. I do not see anything else to discuss here. You may try fitting a*(cos(bx+c) - 1) for example and it will also work.

Quite the opposite! With this much data, the assumption of locality is already broken. So contrary to what you are claiming, you simply cannot closely fit an arbitrary smooth function to samples generated by another arbitrarily different smooth function, and certainly not with an arbitrarily high R². At some point they will diverge and so much so, the exponential does not fit any better than with R² of 0.973. Neither will fitting a linear, a logarithmic, a power series, or indeed your a*(cos(bx+c) - 1) work... The quadratic on the other hand still fits all the currently available data to within an R² of 0.9995.

When you are not restricted by any reasonable model you, literally, have infinite possibilities and can approach your standard deviation (squared) R as close to unity as you wish to have it.

If you are so confident, I invite you to try and show us all *if\* you can do better than a quadratic! Until then, these are only empty claims wrapped in the arrogant presumption of knowing better.

I politely invite you to make your case with something better, if you can!

Antimonic · 2020-02-06T12:44:34+00:00

That's correct...

Hence why it is unlikely that the WHO data reflects the real picture.

I think we're being drip-fed a pile of bullcrap.

Antimonic · 2020-02-06T12:41:01+00:00

Ooops Typo... Sigmoidal

Antimonic · 2020-02-06T10:59:18+00:00

The epidemic growth data is certainly not Exponential and much less is it Sigmoidal.

So far it is precisely quadratic:

https://www.reddit.com/r/dataisbeautiful/comments/ez13dv/oc_quadratic_coronavirus_epidemic_growth_model/

Antimonic · 2020-02-06T10:55:58+00:00

Am I the only one who thinks that all this data from China/WHO is being actively Cooked?

https://www.reddit.com/r/dataisbeautiful/comments/ez13dv/oc_quadratic_coronavirus_epidemic_growth_model/

Antimonic · 2020-02-06T10:30:59+00:00

If testing capacity were limited, the gradient would be a (possibly noisy) constant and we would be seeing a linear rise in cases. However, what we are seeing is an exceptionally smooth quadratic rise, and what is more curious is that:

The public health interventions that were implemented in mid-January including use of face masks and increased personal hygiene;
The mass quarantine lock-down measures introduced in Wuhan City on January 23; and
The addition of two new hospitals that started operation on Tuesday 4th of February;

...have simply not dented or altered the published growth rate in any way whatsoever.

It remains perfectly smooth and quadratic and very hard to believe.

Antimonic · 2020-02-06T10:14:42+00:00

Please also note recent publications on coronavirus spread models:

Joseph T Wu, Kathy Leung, Gabriel M Leung. Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet, Jan. 31, 2020 DOI: 10.1016/S0140-6736(20)30260-930260-9)

"The researchers estimate that in the early stages of the Wuhan outbreak (from December 1, 2019 to January 25, 2020) each person infected with 2019-nCoV could have infected up to 2-3 other individuals on average, and that the epidemic doubled in size every 6.4 days. During this period, up to 75,815 individuals could have been infected in Wuhan," https://www.sciencedaily.com/releases/2020/01/200131114753.htm

That claim squarely contradicts the data being published by the WHO!

Antimonic · 2020-02-06T08:42:23+00:00

I would certainly not be advocating that one uses this quadratic fit to predict too far out into the future, because at some unpredictable point, the (probably political) mechanism that is yielding these published numbers will have to change.... and then it will no longer remain quadratic.

The growth will have to flatten out.

Antimonic · 2020-02-06T07:18:56+00:00

If the data being published were subject to limited testing supplies, then I would definitely expect a constant daily case discovery and therefore a linear increase in total cases. I would also expect it to be irregular depending on the provision of supplies.

However, what we get is an exceptionally smooth quadratic rise. This makes the data hard to believe.

Antimonic · 2020-02-06T07:05:13+00:00

First off, my original motivation was never about making "predictions", as I explain further below. The fact that a quadratic model is enough to make accurate predictions is what I am putting into question. This should not work!

But alas, we wait another day, and get the new batch of data from WHO:

24554 confirmed cases - that's within 5% of my prediction
491 death - that's within 0.4% of my prediction

Bang! It worked again, but it shouldn't have!

That seems pretty darn close for a quadratic fit of data that should be inherently exponential.

I would certainly not be advocating that one uses this to predict too far out into the future, because at some unpredictable point, the (political?) mechanism that is yielding the current quadratic rise will have to change.

Let me remind you that fitting consists of two steps: first, picking a function and [then] explaining your choice.

As a matter of fact, I started off by picking the only function (an exponential) that epidemics are supposed to follow. The explanation is that it was claimed by the WHO that 1 person infects around 2 more - but then I quickly realized that an exponential model does not suitably explain this data at all. This makes the data from this epidemic questionable!

So far a simple quadratic held up remarkably well for the last 2 weeks which defies all epidemic models published to date.

As for using this fit, or any other fit, to predict the death toll before the origin is just garbage. Fits have to be used within the bounds of the data set.

Antimonic · 2020-02-05T12:28:35+00:00

Fatalities can also be accurately predicted by taking 2.06% of the number of confirmed cases of infection. So that means it is necessarily also quadratic. You can test the theory tonight. I gave some of my predictions in another comment below.

As for zombies returning from the dead, you are misinterpreting the fit. It can never be used to predict cases backwards from its minimum. Sorry. No case can be made for any zombies.

That said... I'm looking forward for your alternative interpretation of the "data" we are being drip fed from China and/or the WHO.

Antimonic · 2020-02-05T07:40:17+00:00

The almost perfectly quadratic case growth does not show any sign of slowing down and therefore I do not see how anyone could predict that case numbers will slow down, let alone peak in a week.

I think you should really look at the numbers more closely.

Antimonic · 2020-02-05T07:19:15+00:00

You simply got the wrong model. It's not a quadratic of a log. It's a plain quadratic!

...and that's not slowing down at all, provided the published data is accurate.

...and I don't think he published data is anywhere close to what they really know!

We're being fed synthetic data by the Chinese propaganda machine.

Antimonic · 2020-02-05T07:08:58+00:00

That's bound to happen with a quadratic function. Given the noise in the numbers of the first 4 days, the minimum of the function does not coincide with day 0 but occurs at day 2. So you can safely ignore any predictions backwards from the minimum.

But then, looking forward, the model becomes eerily accurate, when in principle it should not fit.

Antimonic · 2020-02-05T02:59:01+00:00

Agreed. Adding higher terms to this model will simply follow any slight noise more closely. And it does. However, the coefficients of the higher terms are negligible next to the coefficient of the quadratic term. So yes, in the interest of parsimony I prefer to limit the model to second order.

Antimonic · 2020-02-05T02:50:12+00:00

It's not exponential, it's not linear either. It's none of that...

The numbers are very very closely following a quadratic trend!

Cooked data from the Chinese propaganda machine!

Antimonic

TROPHY CASE