COVID Odyssey: Winter Windup 6 ~ COVID-19 Delta Variant 2021 ~ Does Ro = 12?

We look at the how many people one person with the Delta variant of COVID-19 may infect on average in 2021.

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).

Note: Ro and R0 refer to the same thing. For background, read the articles at the bottom of this post.

For the Delta Variant and its predecessors (see first article):



For the original virus in Wuhan Ro is in the range 2.4 to 2.6 (average 2.5).

For the Delta variant Ro is in the range 5 to 8.

For the original virus we obtained Ro = 6 for the original virus.

From the above we estimate Ro may be at least 12 (2 x 6) for the Delta variant since 2.5 x 2 =5 above.

We can use our formula and table to produce our own estimate for Ro for the Delta variant:


We look in the table above and in the second column we see 11.959 is close to 12 and appears when r = 1.70.

We note that SQRT(3) ~ 1.732:


This suggests that for the Delta variant, one person with COVID-19 may infect on average 12.7 other people.

We also note that originally we found that Re = 5.8, suggesting that Re for the Delta variant would be double this, 2 x 5.8 = 11.6, occurring in the table when r = 1.64.

We therefore get a range for Ro for the Delta variant of 11.6 to 12.7 over a 10-day period (n = 10) and a possible daily range for r from 1.64 to 1.73.

This means that without isolation/quarantine the number of cases of the Delta variant may increase each day by between two-thirds and three-quarters and over a two-day period the number of cases may triple.

We may do a simulation to confirm this range.

For the original virus we obtained Ro ~ SQRT(2) which suggests that the number of cases could double in two days.

For the Delta variant Ro ~ SQRT(3) suggests it may be possible for the number of cases to triple in two days.

For background see the articles below:

The cleanest way of comparing the pure biological spreading power of viruses is to look at their R0 (pronounced R-naught). It’s the average number of people each infected person passes a virus on to if nobody were immune and nobody took extra precautions to avoid getting infected.

That number was around 2.5 when the pandemic started in Wuhan and could be as high as 8.0 for the Delta variant, according to disease modellers at Imperial.

“This virus has surprised us a lot. It is beyond anything we feared,” said Dr Aris Katzourakis, who studies viral evolution at the University of Oxford. “The fact it has happened twice in 18 months, two lineages (Alpha and then Delta) each 50% more transmissible is a phenomenal amount of change.”

It’s “foolish”, he thinks, to attempt to put a number on how high it could go, but he can easily see further jumps in transmission over the next couple of years. Other viruses have far higher R0s and the record holder, measles, can cause explosive outbreaks.

“There is still space for it to move higher,” said Prof Barclay. “Measles is between 14 and 30 depending on who you ask, I don’t know how it’s going to play out.”

Click to access 29-june-2021-variants-update-full-report.pdf

Evidence indicates the Delta (B.1.617.2) variant is highly transmissible. WHO data estimates that compared with non-VOCs, Delta may be about 97% more transmissible, and approximately 50-60% more transmissible compared to Alpha (B.1.1.7), specifically.

For more information see:

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