COVID-19 NZ: Could the results in this model occur?

The New Zealand Ministry of Health (MOH) commissioned a number of reports in February and March this year.

One report states that 27,600 would be expected to die in a worst case scenario.

Could this have occurred?

This post considers that report which produced the following results for a worst case scenario:

“Results: In this worse case scenario the epidemic would be expected to peak in early July 2020 (assuming undetected spread since 1 March 2020, see Figure 1).
A total of 3.32 million New Zealanders would be expected to get symptomatic illness; 146,000 would be sick enough to require hospital admission; 36,600 would be sick enough to require critical care (in an ICU); and 27,600 would be expected to die.” See:
https://www.health.govt.nz/system/files/documents/publications/report_for_chief_science_advisor_-_health_-_24_march_final.pdf

We will comment on the report results later in this post.

First we model the results in the report assuming a simple exponential model (instead of a normal curve).

We use a model

d = Exp(rt)
( c.f. Continuously compounded interest)

where:

Exp means e to the power of

e ~ 2.71828 (a mathematical constant)

d is the number of deaths (cumulative) at time t (days)

r is the daily increase, and

t is the time in days since 1 March 2020.

We obtain r = 0.076874386 (see later in this post).

From observations from countries around the world we observe that the cumulative number of  case and deaths follow an S-Shaped curve (e.g. logistic curve).

Therefore we only use the exponential model above up to the midpoint, then we “flip” the earlier results (in reverse) to form an S-Shaped curve (S-Curve).

We obtain the following graphs:

The midpoint is around 3 July (Day 124; Day 0 is 1 March) where the cumulative number of deaths is 13,800 (half of the 26,600 deaths estimated in the report).

At the peak there are about 1,000 (1,021) deaths per day.

You can download pdfs of the above graphs here:
ModelSCurve
ModelBar

For the number of cases we look at the graph on page three the report:

We first note that the peak occurs around Day 104 (not around Day 122 = 1 July).

We also note that 27,600 deaths means over 5,500 (5,520) deaths per million in New Zealand (population 5 million).

Below are the current figures for New Zealand from
https://www.worldometers.info/coronavirus/country/new-zealand/

WORLD / COUNTRIES / NEW ZEALAND

Last updated: May 15, 2020, 09:38 GMT

 New Zealand

Coronavirus Cases:
1,498

Deaths:
21

We currently have about 4 deaths per million.

We look at countries with with the largest number of Cases today. See:
https://www.worldometers.info/coronavirus/

Country	Cases	Deaths	Deaths/ 1 M pop
USA	1,479,019	88,213	267
Spain	274,367	27,459	587
Russia	262,843	2,418	17
UK	236,711	33,998	501
Italy	223,885	31,610	523

We look at countries with with the largest number of deaths per million (see last column).

Country	Cases	Deaths	Deaths/ 1 M pop
San Marino	652	41	1,209
Belgium	54,644	8,959	773
Andorra	761	49	634
Spain	274,367	27,459	587
Italy	223,885	31,610	523
UK	236,711	33,998	501

We also look at US States:

US State	Cases	Deaths	Deaths/ 1 M pop
New York	355,881	27,549	1,416
New Jersey	145,391	10,150	1,143
Connecticut	36,085	3,285	921
Massachusetts	83,421	5,592	811
Louisiana	33,837	2,448	527
District Of Columbia	6,871	368	521

Except for New York, all countries and US states have less than one quarter of the 5,520 deaths per 1M population (27,600 death estimate) for New Zealand in the model.

We leave you to draw your own conclusions.

Below is an excerpt from the report:

Click below to see the whole report:
report_for_chief_science_advisor_-_health_-_24_march_final (1)

Below is the calculation for r (0.076874) for the formula d = Exp(rt):
[ To find r, solve Exp(rt)=27600/2 where t=124 days ]

Estimated Deaths	27600	Report Estimate	Deaths per million
/	2		Deaths/5
	13800	midpoint deaths	5520
ln	9.532424	Natural log of midpoint deaths
Days	124	Days to midpoint
/	0.076874	r

My other COVID-19 posts can be found here:
https://aaamazingphoenix.wordpress.com/tag/coronavirus/

Data for my posts can be found at:
https://www.worldometers.info/coronavirus/
https://en.wikipedia.org/wiki/2020_coronavirus_pandemic_in_New_Zealand
https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide
https://ourworldindata.org/coronavirus-source-data
https://www.webmd.com/lung/news/20200507/100-days-into-covid10-where-do-we-stand
https://projects.fivethirtyeight.com/covid-forecasts/?
https://ourworldindata.org/coronavirus-source-data

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