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

Welcome to My COVID Odyssey.

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.

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.

However it soon became known that a case could be infectious perhaps some days before  becoming symptomatic.

In our simulations we assume an incubation period of one day before a case can infect another person followed by a 10-day infectious period.

Each extra day would add a factor of r to the formula.

The formula was created as a result of averaging 40 simulations. See:

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

For about a year we reduced the incubation period to 0 days. Since we have decided to go back to the original formula. The transfer between the formula it is only necessary to divide or multiply by r.

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


We also have this table:


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 = 6.

This PDF may be easier to read:


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.

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

21 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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