# COVID Odyssey: Worldwide Winter Windup 6 ~ Ro ~ Estimates for the Alpha and Delta variants

We have already estimated Ro for the original COVID-19 Outbreak in 2020 and for the Delta variant.

We have estimated Ro between 5 and 8 for the original COVID-19 Outbreak in 2020.

We have estimated Ro between 9 and 12.7 for the original Delta COVID-19 Outbreak.

We now estimate Ro for the 2020 Alpha variant.

Our chart below shows our (overlapping) ranges for Ro for the variants:

For definitions see the bottom of this post.

Firstly, we look at:

where n = 10 days and r is a high daily growth factor.

Our upper bound for the range for the Delta variant was 12.7 which came from rounding 12.73189 in the table.

We now make this upper bound 12.75 so that the range for the Delta variant for Ro is now 9 to 12.75.

We note that from the table when r = SQRT(2), cases may potentially double every two days.

When r = SQRT(3), cases may potentially triple every two days.

Therefore cases may potentially double every two days for the original COVID-19 and may triple for the Delta variant.

For the alpha variant, we suggest a centre at 8.5 with lower and upper bounds 1.5 on either side of this giving a range for the Alpha variant of 7 to 10.

Alpha is considered 1.5 times as infectious as the original COVID-19.

Delta is considered 1.5 times as infectious as the Alpha variant. See:

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

AUGUST 26, 2021:

“It’s actually quite dramatic how the growth rate will change,” says Dr. Wilson, commenting on Delta’s spread in the U.S. in June. Delta was spreading 50% faster than Alpha, which was 50% more contagious than the original strain of SARS-CoV-2, he says. “In a completely unmitigated environment—where no one is vaccinated or wearing masks—it’s estimated that the average person infected with the original coronavirus strain will infect 2.5 other people,” Dr. Wilson says. “In the same environment, Delta would spread from one person to maybe 3.5 or 4 other people.”

Our estimate for the original COVID-19 outbreak was 5 to 8 for Ro, produced from simulations.

We obtain:

A range for Ro from 5 to 5.667 for the original COVID-19 variant produces
a range for Ro from 7.5 to 8.5 for the original Alpha variant which produces
a range for Ro from 11.25 to 12.75 for the original Delta variant.

The ranges are a factor of 1.5 apart.

Clearly these sub-ranges are within our estimated ranges for the variants.

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).

You may be interested in these tables (see the posts below for the source of the tables):

The Delta variant may be as infectious as measles. From the table above this means Ro must be at least 12. Also see:

COVID Odyssey: Winter Windup 13 ~ Is the COVID-19 Delta variant as infectious as measles?

COVID Odyssey: Worldwide Winter Windup 2~ Be afraid, be very afraid of the Lambda variant

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