Coronavirus Model 3 (Sigmoid curve). Can the Grand Total of deaths in China be less than 4,250?

We use a Sigmoid curve (Logistic function; “S” shape) to estimate the grand total number of deaths in China. Within 2 months from 22 January, we estimate the grand total may be less than 4,250 deaths.

Source:
https://en.wikipedia.org/wiki/Logistic_function

The standard graph looks like this:

We notice that around 18-19 February (Days 27 & 28 from 22 January) the sum of the deaths for these days is 4135 and the totals are relatively stable for pairs of dates above and below these (e.g. Days 26 & 29, 25 & 30).

Update: The above paragraph is no longer considered a suitable method.
For a better approach see:
https://aaamazingphoenix.wordpress.com/2020/03/01/coronavirus-deaths-in-china-estimating-the-midpoint-and-total-number-of-deaths-from-the-data/

An “S-Curve” (Sigmoid curve) has rotational symmetry and therefore f(x)+f(-x) always comes to the same value for all values of x . f(x)+f(-x)=1 for the standard curve above.

The cumulative values up to 18 February form the bottom half of a scaled S-Curve. The same values reversed are added on to the sum for dates above this date.

This results on the following graph:

To see how well an S-Curve fits this curve we roughly fit a scaled S-Curve:

Yes, the shapes are similar.

Day#	Date	Total Deaths	S-Curve Death Estimate	Diff
55	17 March 2020		4,135
54	16 March 2020		4,110
53	15 March 2020		4,094
52	14 March 2020		4,079
51	13 March 2020		4,055
50	12 March 2020		4,029
49	11 March 2020		4,003
48	10 March 2020		3,965
47	9 March 2020		3,922
46	8 March 2020		3,876
45	7 March 2020		3,831
44	6 March 2020		3,773
43	5 March 2020		3,709
42	4 March 2020		3,643
41	3 March 2020		3,570
40	2 March 2020		3,497
39	1 March 2020		3,411
38	29 February 2020		3,322
37	28 February 2020		3,225
36	27 February 2020		3,117
35	26 February 2020		3,020
34	25 February 2020		2,874
33	24 February 2020		2,752
32	23 February 2020		2,609
31	22 February 2020	2,460	2,466	-6
30	21 February 2020	2,360	2,360	0
29	20 February 2020	2,247	2,262	-15
28	19 February 2020	2,126	2,126
27	18 February 2020	2,009	2,009
26	17 February 2020	1,873	1,873
25	16 February 2020	1,775	1,775
24	15 February 2020	1,669	1,669
23	14 February 2020	1,526	1,526
22	13 February 2020	1,383	1,383
21	12 February 2020	1,261	1,261
20	11 February 2020	1,115	1,115
19	10 February 2020	1,018	1,018
18	9 February 2020	910	910
17	8 February 2020	813	813
16	7 February 2020	724	724
15	6 February 2020	638	638
14	5 February 2020	565	565
13	4 February 2020	492	492
12	3 February 2020	426	426
11	2 February 2020	362	362
10	1 February 2020	304	304
9	31 January 2020	259	259
8	30 January 2020	213	213
7	29 January 2020	170	170
6	28 January 2020	132	132
5	27 January 2020	106	106
4	26 January 2020	80	80
3	25 January 2020	56	56
2	24 January 2020	41	41
1	23 January 2020	25	25

Although data is only currently available for a few days after 19 February, the results are encouraging (see Day 30 & Day 31 in the table).

The Death statistics are obtained from:
https://www.worldometers.info/coronavirus/#countries

The totals are for all countries but we use them as figures for China since there have only been about 11 deaths outside China to date.

If the estimates remain reliable over time, the total number of deaths in China (assuming no new outbreak) would appear to be little more than 4135.

As in the previous post we could also estimate the number of deaths using a quadratic up to the halfway point, then reverse these values to calculate the remaining figures.

However since we have official deaths beyond the halfway mark, we may not need to do this.

Clearly the total number of deaths we have calculated is less than 4,250 (less than 4150?).

Time will tell how good this estimate is, and whether we need to treat 4,250 as the total number of deaths or the minimum number of deaths within China.

It all may depend on how well the cumulative death toll may approximated by an S-Shaped curve.

Time will tell.

Alan Grace
24 January 2020

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Is Chinese Coronavirus death data fake news? A quadratic fits well to the data

Many wonder about the accuracy of the Coronavirus data. We look at the number of deaths and find that a quadratic fits very well. Is this coincidence? Is it too good to be true?

Coronavirus data can be found here:
https://www.worldometers.info/coronavirus/#countries

We plot the number of deaths below using the number of days since 22 January 2020:

We develop a quadratic which fits the data:

The equation for the curve is D = 2.78d^2+28 where D is an estimate of the number of deaths and d is the number of days since 22 January 2020.

The factor 2.78 was calculated by by minimising the the sum of the squares of the differences (4960.418 leaving out 17 February, it is however plotted).

The average  difference (Diff) between the actual data and the formula calculations was -0.14 suggesting that this is a useful formula.

We use the formula to estimate deaths in the next 400 days:

The number of deaths appears very low in comparison with other simulations.

We leave you to draw your own conclusions.

We note that, as of the last few days (later after 12 February when the method of diagnosing cases changed from lab tests to xrays, resulting in a spike of over 1400 new cases on that day), the cumulative total number of cases is an average of about 40 times the cumulative total number of deaths each day, down from about 45 times for earlier in February. We use the factor F=40 to estimate the total number of cases (C) i.e. C = 40D and
D = 2.78d^2+28 where D is an estimate of the number of deaths and d is the number of days since 22 January 2020.

The factor F=40 indicates a death rate over 1/40 = 2.5%
(some cases may die at a later date).

We may look further into the factor F in another post when we have more data for d>21 (i.e after 12 Feb). F=40.4 generates only three less cases than reported for 16 Feb (d=25).

We anticipate a vaccine will be available next year, so we may only need to consider up to 400 days (about 18 million people infected, less than 450,000 deaths).

Here is the previous version of the same graph:

Once again the official figures and hence these estimates appear very low. Most simulations calculate millions of deaths (e.g. 65 million) for a similar outbreak.

I leave you to form your own opinion.

I hope the Chinese data is not fake news.

I also hope we do not get infected.

Alan Grace
19 February 2020
https://aaamazingphoenix.wordpress.com/2020/02/19/are-chinese-coronavirus-deaths-fake-news-a-quadratic-fits-well-to-the-data/

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Note: After writing this post I discovered this page:
Lancet nCov2019 propagation model PDF Download (free): 
Lancet nCov2019 Model

and this:

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