COVID Odyssey: Worldwide Winter Windup 8 ~ Ro ~ Estimating Re & Ro by 3 straight lines

We have estimated Re and Ro for COVID-19 using the linear equation y = 17r – 18, where r is a daily growth rate of infections (estimated over the next 5 days).

We now add in two extra lines to complete the approximations. The three lines are:

y = 17r – 18                  r < 1.43

y = 19.1r – 21              r > 1.55

y = 22.7r – 26.6         otherwise

i.e. We use the values calculated for y in the equations as an estimate for Re and Ro.

For definitions see below.

We have estimated r and hence Re for over 175 countries. See:

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

COVID Odyssey: Worldwide Winter Windup 7 ~ Ro ~ Estimating Ro by a straight line

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).

We obtain the table below:


This PDF may be easier to read:


We produce the following chart:


The above straight lines explain why exponential graphs can sometimes appear linear over short ranges. The straight lines cover the curve.

We only require Re and Ro to one decimal place. We use the same formula for both:


where n = 10 days is the number of infectious days.

Below is the original curve (n = 10 infectious days):


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