Banner – COVID Odyssey: Alan Grace's vir[tu]al journey investigating/experiencing life under COVID-19

Updates for New Zealand Delta variant data and results see:

For COVID-19 in the original 2020 outbreak, we have estimated Ro to be in the range 6 to 7.8 based on daily case numbers worldwide up to 6 August 2020.

Below, we extend the range for Ro for the original 2020 outbreak to be from 5 to 8 after reviewing worldwide case numbers on 6 August 2021.

This is the same range (Ro = 5 to 8) that experts have estimated for the Delta variant.

The Delta variant is estimated to be at least twice as infectious as the early 2020 variant.

For the Delta variant we have estimated Ro to be in the range 9 to 12.7.

Ro is the number of people on average one person may infect without quarantine or isolation.

Our estimates for the daily increase, r, for each country are calculated using cases up to 6 August 2020.

Using simulations, we have developed a formula and a methodology to estimate Ro from high values for r using daily case numbers.

We estimate a range for Ro based on our analysis of case numbers for over 175 countries/territories.

In the original 2020 outbreak, assuming with an infectious period of n = 10 days, we have (using our formula for Ro below):

For Turkey, r = 1.52, and Ro = 8
For China and the USA, r = 1.5 and Ro = 7.8 based on r = 1.51
For New Zealand, r = 1.4, Re = 5.8, and Ro = 6 when r = SQRT(2)
For the UK, r = 1.3575, and Ro = 5

The above give us our range for Ro.

For r = SQRT(2), Ro = 6.0 (1 dp) using the formula, we may have case numbers doubling every two days.

For r = SQRT(3), Ro = 12.7 (1 dp), we may have case numbers tripling every two days (for the Delta variant).

The figures for the 31 countries below were retrieved on 6 August 2021 from
https://www.worldometers.info/coronavirus/#countries

Highest 31 Countries by case numbers

Highest 31 countries ranked by r

All countries ranked by r

All Countries alphabetically

COVIDWorldAllCasesCPM

COVIDWorldAllCasesCPMPop

Daily values for r for each country were estimated using Excel once case numbers were at least 30. For our methodology for estimating r, see:

https://aaamazingphoenix.wordpress.com/2021/08/05/covid-odyssey-worldwide-winter-windup-covid-19-in-2020-how-many-people-may-one-person-infect-in-your-country/

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)
a 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 considered widening our range estimate for COVID-19 in early 2020 after looking at world case numbers up to 6 August 2021. See:

https://aaamazingphoenix.wordpress.com/2021/08/02/covid-odyssey-winter-windup-12-conclusion-ro-6-to-7-8-in-early-2020/

We accept a range for Ro in early 2020 between 5 and 8 to include Turkey and the UK.

We note that the range 5 to 8 is the same as the estimate for the Delta variant in the image below:

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

We calculate Ro from r using our formula:

We assume n = 10 days and that infectivity decreases daily at a rate of 1/r.

We would need a range for Ro from 4 to 8 to hopefully include all 31 countries in the lists below except India, Iran, and Iraq. We consider this range may be too wide to be acceptable.

Australia would also still be excluded.

The results are considered together with the 31 countries with over 1,000,000 cases of COVID-19 on 6 August 2021.

The lists in the tables below contain all 31 countries with over 1,000,000 cases of COVID-19 on 6 August 2021. See:

https://aaamazingphoenix.wordpress.com/2021/08/15/covid-odyssey-worldwide-winter-windup-covid-19-in-2020-vs-2021-cases-per-million-people/

See also:

Highest 31 Countries by case numbers

Highest 31 countries ranked by r

All countries ranked by r

All Countries alphabetically

COVIDWorldAllCasesCPM

COVIDWorldAllCasesCPMPop

In the tables above Re#2 is an estimate for Ro, calculated using our formula for Ro:

We assume n = 10 days and that infectivity decreases daily at a rate of 1/r.

We have used simulations in Excel to create the formula. See:

https://aaamazingphoenix.wordpress.com/2021/08/17/covid-odyssey-winter-windup-14-covid-19-simulations-to-develop-our-formula-for-ro/

We also consider:

https://aaamazingphoenix.wordpress.com/2021/08/16/covid-odyssey-winter-windup-13-is-the-covid-19-delta-variant-as-infectious-as-measles/

Experts think the COVID-19 Delta variant is much more contagious than the flu and chickenpox, and on par with the measles. See:
https://www.healthline.com/health-news/cdc-says-delta-variant-as-infectious-as-chickenpox-what-to-know-now

For these values of Ro and herd immunity thresholds (HITs) of well-known infectious diseases prior to intervention, see:
https://en.wikipedia.org/wiki/Basic_reproduction_number

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 chosen n = 10 days. In the tables below, if n > 10 days, the values for Ro are likely to be too high to be acceptable.

We have also used this version:

Note:

Ro = 8 corresponds to r = 1.52, near the r = 1.5 estimated for China, The USA, and South Korea.
Ro = 6 corresponds to r = SQRT(2), near the r = 1.4 estimated for New Zealand, Italy, France, Norway, and Poland.

Reminder:

For r = SQRT(2), Ro = 6.0 (1 dp), we may have case numbers doubling every two days.

For r = SQRT(3), Ro = 12.7 (1 dp), we may have case numbers tripling every two days (for the Delta variant).

For the Delta variant, we have estimated Ro to be in the range 9.0 to 12.7 (1 dp).

For our methodology to estimate r for countries, see:

https://aaamazingphoenix.wordpress.com/2021/08/05/covid-odyssey-worldwide-winter-windup-covid-19-in-2020-how-many-people-may-one-person-infect-in-your-country/

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

https://www.healthline.com/health/r-nought-reproduction-number#covid-19-r-0

The above website mentions this article which estimates a median value for Ro of 5.7:
https://wwwnc.cdc.gov/eid/article/26/7/20-0282_article

We find that the range 5 to 8 for Ro is likely to be conservative because:

the 5 and 8 are based on values for Re with no increase for estimating Ro
The number of infectious days is only n = 10
The infectious days start before cases are symptomatic

I believe that New Zealand has done the right thing moving to Lockdown Level 4 quickly this week when a case of the Delta variant was discovered in the community.

Let’s hope New Zealand does not need to stay in Lockdown Level 4 for a lengthy period.

Alan Grace
18 August 2021

PS For a list of all my posts (pingbacks) see:

https://guestdailyposts.wordpress.com/guest-pingbacks/

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)
a 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: