We need to have a way of measuring if the progress of the percentage of fully vaccinated people may be sufficient to achieve a target of 80% or 90% fully vaccinated within a desired timeframe, say the end of the year or at the end of February.
We suggest the calculations based on v(f – v) may provide a suitable indicator.
The following graphs may be suitable:
The graphs were both produced from this table:
Note: x(f-x) should be v(f-v) throughout
At the end of September, New Zealand had almost 38% of the population fully vaccinated.
We probably need to exceed the f = 1.95 curve until the end of November (> 81% required) to allow for a flattening of the curve in December should it be possible to reach 90% vaccinated this year.
September (month 1) means at the end of September.
We suggest for each month we calculate
v[i+1] = v[i] ( f – v[i] )
where v[i] denotes the vaccination target at the end of the month i.
This may look confusing.
Percentages are changed to decimals.
38% becomes 0.38 (for September)
For the next month, the required vaccination level is calculated using
v = 0.38 to obtain using f = 1.90
0.38 ( 1.90 – 0.38 ) = 0.5776
i.e. 57.76% vaccination level for the next month (October).
Start with v1 = 0.38 and f = 1.90
v2 = v1 ( f – v1)
v2 = 0.38 ( 1.90 – 0.38 )
v2 = 0.5776 (from the table 57.76%).
v3 = v2 ( f – v2)
v3 = 0.5776 ( 1.90 – 0.5776 )
v3 = 0.7638 (from the table).
There is nothing scientific about the formula.
What about the f = 1.90?
If we are interested in achieving 90%.
90% as a decimal is 0.90
We add on 1 and use f = 1.90 in calculations.
In the last column of the table for f = 1.90 we see 89.96% which is almost 90%.
Compare the other values for f and the last column.
Where does the 38% come from?
For the complete set of tables and graphs (some are repeated for convenience in comparisons) see this PDF:
Do you think this approach is good for indicating if a country is on track to achieve a required vaccination percentage? If not, what do you suggest instead?
To achieve the desired vaccination percentage earlier, perhaps add on 0.03 or 0.05 to f.
e.g. For 90%, instead of f = 1.90, we could use f = 1.93 or f = 1.95.
We find that f = 1.93 works well to achieve 90% by the end of December starting with 38% vaccinated (0.38):
After rounding to achieve 90% fully vaccinated by the end of December, we would need 60% fully vaccinated by the end of October and 80% fully vaccinated by the end of November.
We would probably need to exceed these targets because the theoretical results do not factor in an expected flattening of the curve especially above 80% as a result of groups reluctant to get/not interested in getting jabbed: Maori, gang members, rough sleepers, people in prison, and anti-vaxxers etc.
As we have already stated, we probably need to exceed the f = 1.95 curve until the end of November (> 81% required) to allow for a flattening of the curve in December should it be possible to reach 90% vaccinated this year.
Earlier on last week the percentage was 33.33% so we also include tables and graphs above for this percentage in the PDF above.
Below we Have graphs and tables for 80% ( f = 1.80) and 90% ( f = 1.90).