COVID Odyssey: Winter Warning NZ 10 ~ Delta variant ~ Analysis

We analyse the 2021 outbreak in New Zealand. We hope that the midpoint has been reached.

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).

In New Zealand we have found a daily rate of increase of r ~ 1.4 (40% increase per day) in March and assume a 10-day infectious period (when a case can infect others).

We assume a daily increase of r (e.g. r = 1.4 in early 2020) and a daily decay in infectivity of 1/r over a 10-day infectious period for each case (n = 10).

We look at the graphs below (they  all use the same data):

Graph 1

NZCasesDeltaChart3

We see in Graph 1 that r = SQRT(2) fits the data well until the curve starts to flatten a little.

We see an indication of flattening when r = SQRT(2) starts to cross the curve r = 1.4.

The curve remains exponential.

The highest two curves indicate the number of cases for a Delta outbreak without isolation/ Lockdown or quarantine.

New Zealand went into Lockdown Level 4 at 11.59 pm om Tuesday 17 August 2021.

Graph 2

NZCasesDeltaChart2

Graph 3

NZCasesDeltaChart1

The curve r = 1.57 shows that there may have been almost 10,000 cases theoretically on Day 20 (30 August) if NZ had not gone into Lockdown Level 4.

We see that r = SQRT(2) works for 21 August to 25 August.

NZCasesDelta31Aug

We see in the above table (column r = 1.57) that if we had not gone into Lockdown we could maybe theoretically have had 1,000 cases on 25 August and 15,000 cases on 31 August. The figure of 15,000 potential cases was mentioned by the NZ Prime Minister Jacinda Ardern in the TV COVID-19 media update on Monday 30 August.

After the curve starts to flatten the data still remains exponential. See:

NZCasesDelta31AugB

NZCasesDelta1100Chart29Aug

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

We assume a person may be infectious for n days once they become symptomatic (show symptoms). A person may be infectious for at least two days prior to becoming symptomatic.

We assume a 5-day cycle where the incubation period is one cycle long (until symptoms appear) and the infectious period is two cycles long.

In New Zealand we have found a daily rate of increase of r ~ 1.4 (40% increase per day) in March and assume a 10-day infectious period (when a case can infect others).

We assume a daily increase of r (e.g. r = 1.4) and a daily decay in infectivity of 1/r over a 10-day infectious period for each case.

We see r =1.4 works well in early 2020 prior to Lockdown Level 4 at 11.59 pm on 25 March 2020.

We obtain the estimates below using actual NZ cases in the initial 2020 outbreak.:

NZRoTableAV

We estimate Ro using the formula:

Ro

TableRe2021C

We have seen that Ro = 5 to 8  corresponds to the original 2020 outbreak.

We estimate Ro = 9 to 12.7 (r = 1.57 to SQRT(3) ) corresponds to the 2021 Delta outbreak. See:

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

Compare these values with the estimates below:

Delta

We hope that the midpoint for this outbreak has been reached. Remember that in the original 2020 outbreak there were two peaks. See:

COVID Odyssey: Winter Warning NZ 5 ~ Estimating the number of 2021 Cases ~ Where will the midpoint be?

Also see:

https://aaamazingphoenix.wordpress.com/?s=winter+warning+nz

https://aaamazingphoenix.wordpress.com/?s=windup

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