# COVID Odyssey: Winter Windup 10 ~ COVID-19 Delta variant ~ Conclusions 2021

The Delta variant of COVID-19 appears to be twice as infectious as the original 2020 outbreak.

We have found that Ro for the Delta variant is between 9 and 12.7.

Ro is the average number of people once person may infect over a period of n = 10 days when there is no quarantine or isolation.

We may in future need more than two jabs of vaccine.

We have always found that a daily increase of r = 1.4 for estimating COVID-19 cases in New Zealand works well up until the day after Lockdown Level 4 started at 11.59 pm on 25 March 2020.

For estimating Ro we assume that the number of cases continues to increase everyday at the daily rate, r, and infectiousness decreases daily at 1/r.

In reality this does not happen so Re can be far less than Ro except maybe near the beginning of an outbreak.

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 always found that a daily increase of r = 1.4 for estimating COVID-19 cases in New Zealand early in 2020 works well up until the day after Lockdown Level 4 started at 11.59 pm on 25 March 2020:

For 11 days the actual case numbers are close to the estimates using r = 1.4 (starting with an estimated 10 cases).

We also realised that our original formula/calculations for Ro were best.

For the 2020 outbreak of COVID-19 we estimated Ro = 6.

We now look again at the 2021 Delta variant of COVID-19.

In previous posts we simulated outbreaks using a value for Ro around 12.7 (actually Ro = SQRT(3)).

In this post we consider also Ro = 9 (halfway between 6 and 12) to get a range for Ro for the Delta variant from 9 to 12.7.

Please look at the last column of the table below. The last column  has values of Ro for an infectious period of n = 10 days.

For the initial outbreak we calculated from the table Ro = 6 for a daily rate of increase in infections of r = SQRT(2).

For the Delta variant in previous posts we calculated Ro = 12.7 corresponding in the table for a daily rate of increase of r = SQRT(3).

The Delta variant of COVID-19 appears to be twice as infectious as the original 2020 outbreak.

Since this is not definitive, we need to consider a range for Ro for the Delta variant.

We consider Ro =9, the value for Ro halfway between 6 and 12.

We see in the above table that Ro = 9 corresponds to a daily rate of r = 1.57 to get a range for Ro for the Delta variant between 9 and 12.7.

It is probably easier to start at n = 7 for r = SQRT(3) to get a similar range 9 to 12.7.

Using n =7 days gives a value for Ro about 25% less than the value for n = 10 days.

The range for Ro from 9 to 12.7 corresponds to values for n = 7 and n = 10.

We now consider the range for Ro for the Delta variant in the table below.

Remember that a person may be infectious days before being symptomatic (showing symptoms).

Assuming that contact tracing, quarantining and isolation of cases may halve the effective number of infectious days, we look at the first column in the table (n = 5) to get a value for Re (the effective Reproduction number).

Corresponding to r = 1.57 we get Re = 5.

For the upper value in the range, we look at n = 6 days (one day later).

Now look at n = 6 in the table. For r = SQRT(3) in the last row, the table gives Re = 7.9.

This gives a range estimate for Re of 5 to 7.9, similar to the values for Ro for the Delta variant estimated in the range 5 to 8 below:

i.e. One person may effectively infect 5 to 8 other people. Re in our analysis may be in the range 5 to 8.

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‘As transmissible as chickenpox.’ Here’s the CDC report on the delta variant that led to new mask policy. – MarketWatch

Introduction to Disease Ecology: Measuring the Impacts of Diseases and their Control (jhsph.edu)

Why R0 Is Problematic for Predicting COVID-19 Spread | The Scientist Magazine® (the-scientist.com)

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https://www.yalemedicine.org/news/5-things-to-know-delta-variant-covid

https://www.bbc.com/news/health-57431420