# 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.

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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