COVID Odyssey: Worldwide Winter Windup ~ COVID-19 in 2020 vs 2021 ~ How many people may one person infect in your country?

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 the next 5 days 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.

Our estimates for Ro for the initial 2020 outbreak are comparable to estimates elsewhere for the Delta variant. See:

COVID Odyssey: Winter Windup 12 ~ Conclusion~ Ro = 6 to 7.8 in early 2020?

A year on from the cut-off date in our original dataset, we combine our results with the latest cases (6 August 2021) for all 31 countries with over 1,000,000 cases.

We first look at case numbers for 185 countries, eight which we could not analyse due to insufficient case numbers.

Our values calculated for r for China and New Zealand are similar to those estimated in the previous post.

The r^5 column below is the rate of increase in case numbers over a 5-day period.

The results for the top 27 countries are below:



The curves cross at around
r = 1.506424117

Also see these PDFs:



We could not analyse eight countries/territories due to insufficient case numbers by 6 August 2020:


These PDFs include dates and case numbers:





A year on from the cut-off date in our original dataset, we combine our results with the latest cases (6 August 2021) for all 31 countries with over 1,000,000 cases on this site:


Highest 31 Countries by case numbers

Highest 31 countries ranked by r

All countries ranked by r

All Countries alphabetically


Maybe see the results for your country in the above files. Countries are listed alphabetically by three letter country code in files with ALPHA in their name.

First for each country we estimated r, the daily rate of increase in case numbers based on 5-day intervals. We averaged each consecutive pair of estimates and found the maximum value.

We limit our calculations to days where:

  • Case numbers (cumulative) are at least 30
  • Our value for r is less than 1.6

Note: averaging from the previous day may still use and result in a value above 1.6.

The last column (Re#2) in the above table estimates Ro using the formula in the table below.

Also see these other posts:

Let C[D] be the cumulative case numbers for Day D.

For each country, for For each Day D, we calculate

r[D] = ( C[D+5] / C[D]  ) ^ (1/5)

where ^ means to ‘the power of’.

For each consecutive pair of values for r[D] we calculate

r = Average( r[D] ,  r[D+1] ) and find the maximum value for r.

We use this maximum to estimate Re#2 and hence Ro.

Data source for calculations:
retrieved 7 August 2021 from

We concluded earlier that r ~ 1.51 will provide a good value to calculate Ro using China case numbers.

From the table below we see that for r = 1.51, Ro ~ 7.8.


In New Zealand we have already seen that r = SQRT(2) works well and gives R0 ~ 6.

We concluded that in early 2020 Ro is likely to be in the range 6 to 7.8.

The analysis in this post helps to confirm Ro is likely to be in this range.

We note that in the table Re = 5.8 corresponds to r = 1.4. We expect Ro to be greater than this, in a range starting at least with r = SQRT(2) and hence Ro = 6. Our range is similar to the top half of the 95% Confidence Interval (95% CI) below (although our serial interval is less):

Thus, these results suggest a serial interval of 7–8 days. With this serial interval, we sampled latent and infectious periods within wide biologically plausible ranges (Appendix 2) and estimated the median R0 to be 5.8 (95% CI 4.4–7.7) (Figure 5, panel A)

See this article and its abstract:

We have already estimated Ro for the Delta variant to be between 9 and 12.

This suggested that Ro for the Alpha variant may be centred around 8.4; maybe in an overlapping range of 7.4 to 9.4.





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: If we change r[d]<1.6 to r[d]<1.7 we do get some changes in the results. The table below is sorted by the last column
r* = ( r[d] and r[d+1] )/2 :


We prefer to use r[d]<1.6.

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6 Comments Add yours

  1. AlanGraceNZ says:

    Reblogged this on COVID Odyssey by Alan Grace: My vir[tu]al COVID-19 journey and commented:

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

    Come back later today to see the results.


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