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.

SCurveWiki1

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

The standard graph looks like this:

SCurve

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:

CorDeathSC

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

CorDeathSCfitted

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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