New Zealand went into Lockdown Level 4 (L4) at 11.59 pm on Wednesday 25 March.
In this post we analyse what may have happened if L4 had been delayed one week.
We find a curve that fits the total number of cases.
First we look at the ratios of the total number of cases (see table later).
For Days 18 to 26 the average ratio is Av = 1.45339379.
We consider the equation
C = 10a^(D-18)
^ means to the power of,
C is an estimate for the Total number of Cases at Day D, and
a is near Av.
Instead of the constant 10, we also looked at using 8 and 9.
Using a = 1.4 gave the most useful results and matched well up until Day 28.
i.e. Staring with 10, we keep multiplying by 1.4 to obtain successive estimates for C (for each Day D).
For 5-Day cycle this gives a value R of
1.4^5 = 5.37824
We note that while on Day 26 (24 March) the estimate in the table is 8 below the actual number, two days before out estimate is 9 above the actual number, perhaps suggesting a delay in contact tracing(?).
As in previous posts we create a table:
(model starts with a total of 10 cases- extra numbers backfilled)
This time we generate the values for the Total column, starting at 10, then subtract to create the estimate for the ‘daily number of cases for each cycle (New Est) after generating the values before 10.
The ratio R for both columns is the same, so we also generate the value 0.28, slightly different by .07 than the matching value in the next column (0.35).
We decide that it is best to maintain the ratio and therefore retain the values.
Below is the daily graph:
Below is an enlarged version:
The current number of cases yesterday was 1,503 (very close to the final total).
On 31 March the estimated total is 1,555.
If the midpoint is this early we double this total to obtain a final total over 3,000 which is more than double our existing total.
We note that the actual midpoint for cases appears to be around 1-2 April.
If the midpoint for our estimates are around these dates than the estimated total number of cases becomes over 4,000 and 6,000 cases or 5,000 if, as in the past, we add the values together. c.f. 708 + 797 = 1505 (very close to 1503).
Lockdown appears to have flattened the curve far sooner than expected earlier.
In another post we may look at what relationship the value R may have to Ro, the infection rate.
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