# 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:

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.

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

# 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:

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 9.53242 Natural log of midpoint deaths Days 124 Days to midpoint / 0.076874 r

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