# COVID Odyssey: Winter Warning NZ 9 ~ C = ar^d ~ A trivial way to estimate total case numbers

We have used the formula C = ar^d to estimate case numbers in New Zealand.

The easiest was to calculate C is to start with the value a, and on each successive day multiply the previous day’s estimate by r.

In last years initial outbreak we saw in New Zealand r = 1.4 and r = SQRT(2) worked well for a daily rate.

For a, we use a = 1, and a = 1.6.

We obtain the table below.

Note: This would be an estimate which we assume could be made early in the outbreak. i.e. It is not a current estimate.

CasesEst2

In the early 2020 outbreak in New Zealand, we had a maximum of 89 new Cases.

So, we highlight in the above table where the number of new cases first exceeds 100 as well as the new cases for the previous day.

This gives us a range from 70 to 125 new cases near the peak, and say 350 to 430 corresponding total cases.

Note: For the total cases we are using the over 100 new case values to reduce the range.

Presently we have around 82 new cases on the previous two days.

On Saturday we reached a total of 429 cases and on Sunday 511 cases:

NZCases2021Aug30

The first table could have been obtained very early in the outbreak as a rough estimate.

Does this indicate we are near the midpoint?

The rough estimate of 750 to 1000 cases in total is likely to be exceeded since we already have 511 cases, suggesting the total is likely to be in the range 1000 to 1200 and more if the midpoint has not been reached.

We expect the table to provide estimates that may be expected to be low since the values for r are based on 2020 cases. We expected higher values since the Delta variant will have a higher value for Ro.

The table has produced results that may be similar to early estimates produced by experts.

The first table shows a possible peak around day 16 to 18. Yesterday was day 19.

Does this suggest we may be close to the midpoint?

It is surprising that going to Lockdown Level 4 early has produced the values r = SQRT(2) and a = 1.16 to closely estimate actual case numbers.

Also see:

COVID Odyssey: Winter Warning NZ 8 ~ 2021 Delta midpoint ~ Are we there yet?

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