# COVID Odyssey: Winter Warning NZ 13 ~ Delta variant ~ Estimating r, Re and Ro

We have looked at data for 175 countries around the world and estimated r and Re for those countries. We apply the same heuristic for this years Delta outbreak in New Zealand.

Read the reblogged post (below this post) for the background.

Here are the calculations applied to the 2021 Delta variant outbreak in New Zealand:

Read the reblogged post below to see the way the computations below work.

Note that n = 10 days and  r[d] is a daily increase (growth factor) calculated over the next 5 days starting on day d for each country, and C[d] is the total number of Cases on Day d of the outbreak.

For more definitions see the bottom of this post.

We assume that infectivity decreases daily at a rate of 1/r.

The biggest number in the last column of the table is  r =1.43444. We use this to estimate Ro.

This is bigger than our value for this Delta outbreak of r = SQRT(2) or r ~ 1.4142.

We therefore suggest changing the step

r = max { ( r[d] + r[d+1] )/2 } to

r = max { 0.25 x r[d] + 0.75 x r[d+1] }

This would give the estimate

r = 1.418598

which is much closer to

r = SQRT(2)

~ 1.4142

The change to

r = max { 0.25 x r[d] + 0.75 x r[d+1] }

will have minimal effect for most countries.

Our revised computations are:

For New Zealand in the early 2020 outbreak the value estimated for r changed from 1.39846 to 1.40086, closer to the desired 1.4 using the above change.

From r we can calculate Ro using the formula or the last column in the table below:

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).

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We look again at the spread of COVID-19 throughout the world early in 2020. We look at case numbers up to 6 August 2020. As expected estimates for Re#2 (last column in the first table, calculated using our formula for Ro below), and hence Ro occurred very early in an outbreak in each country.

Ro is the average number of people one person with COVID-19 may infect when there is no quarantine or isolation. Our simulations have verified that the formula below for Ro is theoretically correct.

Note:  r is a daily rate of increase (growth factor) calculated over a 5-day period for each country, and C[d] is the number of Cases on Day d of the outbreak for each country.

We assume that infectivity decreases daily at a rate of 1/r.

Using Excel, we used our formula to estimate Ro from the daily growth rate, r, for 185 countries.

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