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

We estimate 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). i.e. We use the value calculated for y in the equation as an estimate for Re and Ro.

Update: See:

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

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).

Please look at the chart below: We have the following formula for estimating Re and Ro: Where n = 10, the number of infectious days.

The above chart was created using this table: We can just add 0.1 to the value of Ro to get a better estimate if r is outside the range r = 1.33 to 1.46.

This means the straight line becomes y = 17r – 17.9 when r is outside the range r = 1.33 to 1.46.

It’s easier just to add 0.1.

Note that the estimate for New Zealand when r = 1.4 for the early 2020 outbreak is very good.

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