Welcome. My COVID Odyssey posts prior to April 2022 have now become an open time capsule.

My COVID-19 posts can also be found here:

My name is Alan Grace. I live in Titirangi (Auckland, New Zealand).

Welcome to Alan’s Ark, The Amazing Phoenix, and My COVID Odyssey (all on this site).

For a timeline of COVID-19 in New Zealand see:

There are many methods that can be used to model COVID-19. You can find some in this post:

COVID-19: Methods of Analysis

In my own undergraduate and postgraduate study I enrolled in papers in numerical analysis and differential equations.

Instead I now tend to use (relatively) simple maths to look at actual case data.

By definition we let:

  • r denote the effective Reproduction rate of COVID-19 for one day; r is the growth in the number of cases. We usually calculate r (for one day) using the rise in cases over the next 5 days.
  • 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). Ro and Re both use this formula:


where n = 10 infectious days. Define Ro =1 when r =1 (to avoid a divide by zero).

We assume that infectivity reduces by a factor of 1/r each day.

Historically we have assumed three 5-day cycles:

  1. A 5-day incubation period after which a case becomes symptomatic.
  2. Two 5-day cycles during which a case is infectious.

It is known that a person can be infectious some days before  becoming symptomatic.

Hence in our simulations we assume a very small incubation period before a case can infect another person followed by a 10-day (two 5-day cycle) infectious period.

We assume that if a person is infected on say Monday, the person would not transmit COVID-19 to another person until Wednesday.

Any additional (incubation) day would add a factor of r to the formula.

Our formula was created as a result of averaging the means of 40 simulations. See:

COVID Odyssey: Winter Windup 14 ~ COVID-19 ~ Simulations to develop our formula for Ro

For about a year we did not have an incubation period. Since then we have decided to go back to the original formula. The transfer between the formulae it is only necessary to divide or multiply by r.

Below please find values for r (daily growth) and corresponding values for Re:


Originally we also obtained the table below calculating Ro based on r and Re
(generally, to be conservative, we will continue to use the above table).

COVID Odyssey: NZ New Year Fear 17 Post #944~ COVID-19: Calculating Ro based on Re Case numbers


This table calculates Ro based on n = 9 days.


This suggests that Ro for the original variant of COVID-19 is very likely to be in the range 5 to 8.

For New Zealand and many other countries, r = 1.4 and Ro = 7.1.

We note that on day 10 for r = 1.4 case numbers without isolation are slightly more than double actual case numbers with isolation and more than triple when r = 1.73 onwards, with all case numbers without isolation (for r > 1) around a factor of r squared (slightly more) times the case numbers with isolation.

Starting with 10 cases, this means we can estimate the number of cases without isolation on day 10 as 10r^12 (and 10r^10 with isolation).

To estimate Ro we can therefore use in our formula r = (r^12)^(1/10) or r^1.2.

For an estimated daily increase of r, we can estimate Ro to be in the range calculated using our formula using r between r and r^1.2 (with Ro rounded say to 2 d.p.).

We obtain:


This PDF may be easier to read:


Originally we obtained:


COVID Odyssey: NZ New Year Fear 14 Post #941~ COVID-19: A table comparing Ro and Re

For worldwide estimates for r, see:

COVID Odyssey: Worldwide Winter Windup 5 ~ Revised estimates for Re worldwide

We have used this chart to estimate Re and Ro for various variants. Below is our latest version:


Also see:

COVID Odyssey: NZ New Year Fear 38 Post #965~ NZ COVID-19: Revised calculation for Ro

COVID Odyssey: NZ New Year Fear 33 Post #960~ NZ OMICRON: Is Omicron as infectious as the measles?

COVID Odyssey: Summer Surprise 2 ~ Post#924: NZ COVID-19~ OMICRON has reached NZ border

For original 2020 variant of COVID-19 worldwide (weighted) rankings see:


The rankings above for columns r# and Re# use these calculations:

r0formula (1)

COVID Odyssey: Winter Warning NZ 13 ~ Delta variant ~ Estimating r, Re and Ro

Note that n = 10 days and  r[d] is a daily increase (growth factor) calculated over the next 5 days starting on day d for each country, and C[d] is the total number of Cases on Day d of the outbreak.

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:


Also see:


Also see these polls:











Also see:

COVID Odyssey: New Year Fear ~ Post #928: How sky high are these PI hypotheses?

COVID Odyssey: Summer Surprise 2 ~ Post#924: NZ COVID-19~ OMICRON has reached NZ border

COVID Odyssey: Worldwide Winter Windup 5 ~ Revised estimates for Re worldwide

COVID Odyssey: Worldwide Winter Windup 9 ~ Ro > Re ~ How much greater is Ro?

COVID Odyssey: Winter Windup 5 ~ Conclusions for NZ in 2020 ~ Back to the past: Re = 5.8 and Ro = 6

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

Please obtain prior written permission from the author (Contact me) before publishing or copying anything from this site on any another site or anywhere else (Reblogs OK).

Please read the Disclaimer.

Please note: any ads are beyond my control 😦

Rather than take up screen real estate at the top of my Home page, I have put my Welcome page on this separate page so that you don’t need to scroll down past it all the time (this is one of my pet hates; having to scroll down when there are large images at the top of a page).

I like Escher’s work. Surreal.


See more here.

View more in Google

View some more in Google

Go back to my home page.

My posts often change. I cannot resist tinkering and updating.
My posts (especially poems) seldom stay static. Come back to see the changes.

You may like to view: My ‘First’ post (formerly Alan Grace: Header Post)

Enjoy my Blog.

Alan Grace



Wordplay … Poetry in Progress.

The AAAmazing Phoenix



Farewell The AAAmazing Phoenix

45 Comments Add yours

  1. Sorry! My schedule is nuts today so perhaps this is why the prompt rules are not clicking with me. Good luck!


    1. AlanGraceNZ says:

      To share your own post, just put the following line anywhere in your post:
      (Click on the same link to view posts)

      Liked by 1 person

    2. AlanGraceNZ says:

      You’re welcome Martha. The easiest think to do is just put the link into one of your existing posts and watch the magic happen 😉


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