COVID Odyssey: Winter Warning NZ 2 ~ Delta variant ~ Lockdown 4 appears to be working

Lockdown Level 4 appears now to be starting to bring down the daily rate of increase (r) of case numbers of COVID-19 in New Zealand.

Update: See:

COVID Odyssey: Winter Warning NZ 6 ~ Estimating the number of 2021 Cases ~ A simpler formula

ee the last column in the table below where values for r are starting to decrease after almost reaching 1.5.


Today (23 August) we have 107 cases in the community.

Before the case numbers were released (announced around 1 pm) we estimated (before r started decreasing) that there would be from 115 to 125 cases.

For 25 August we estimated from 250 to 300 cases and for 31 August maybe 2900 to 4600 cases were possible if the daily rate had not been decreasing or Lockdown does not stay at Level 4 at least for Auckland. There is an announcement later today about what the Lockdown levels may be throughout the country from tomorrow night.

Fortunately Lockdown appears to have slowed down the daily rate of increase (see last column in the table).

Estimates for r, the daily rate of increase are based on the rate of increase from 13 August where we appear now to have had a total of 2 known cases in the community.

If we have a total of C cases d days later, then r was calculated as

r = (C/2)^(1/d).

Also see:


The equations for the curves in the graphs below are:

C = ar^d + c

where ^ means ‘to the power of’

r = 1.5,    a = 0.8830,  c = 0.12, and

r = 1.57, a = 0.5540 , c = 0.64

r = 1.5 gives us an estimate for Re (7.6) when n = 10 days and

r = 1.57 gives us an estimate for Ro (9).

See these graphs (the second graph is a zoomed in version):



For the Delta variant worldwide, we have estimated Ro to be in the range 9 to 12.7.

Ro is the number of people on average one person may infect without quarantine or isolation. For more definitions se below.

For the current Delta outbreak in New Zealand we estimate that one person may on average infect 9 other people (Ro = 9).

We calculate Ro and Re from r using our formula:


We assume n = 10 days and that infectivity decreases daily at a rate of 1/r.

By definition we let:

  • r denote the effective Reproduction rate of COVID-19 for one day
  • Ro (R0; R-Zero; R-Nought) denote the Reproduction number for COVID-19 without any quarantine or isolation
  • Re denote the effective Reproduction number for COVID-19
    (Re assumes isolation/quarantine is happening)
  • case be defined as a person diagnosed as having COVID-19

Note that Ro and Re are numbers (not rates), the number of people one person with COVID-19 may infect on average without quarantine or isolation (Ro) and with quarantine or isolation (Re).

We have chosen n = 10 days (first column). In the tables below, if n > 10 days, the values for Ro are likely to be too high to be acceptable.


We have also used this version (see last column):


For the current Delta outbreak in New Zealand, we conclude that one person may on average infect 9 other people (Ro = 9).

You may like to look at:

COVID Odyssey: Winter Windup 15 ~ Executive summary ~ Our formula for Ro

I believe that New Zealand has done the right thing moving to Lockdown Level 4 quickly this week at 11.59pm on Tuesday 17 August  when a case of the Delta variant was discovered in the community.

Let’s hope New Zealand does not need to stay in Lockdown Level 4 for a lengthy period.

Sadly at least Auckland may need to stay at Level 4 for at least a few more weeks.

Alan Grace
23 August 2021

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