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

We have used simulations to develop our formula for Ro which is based on the daily rate of increase, r, for cases. For simulations using r = 1.4 and r = SQRT(2), for each simulation we generate 40 outbreaks using Excel and calculate statistics. Sample runs are included in this post.

Our formula for Ro was developed from the simulations.

For simulations for r = SQRT(3), only one outbreak was simulated each time.

We produce the formula where n = 10 days (see the last column in the table below).

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.

For estimating Ro we assume that the number of cases continues to increase everyday at the daily rate, r, and infectiousness decreases daily at 1/r.

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). Below are sample results.

For r = 1.4

CSAWsim (30 more rows)

CSAWsimB

For r = SQRT(2)

CSAWsimSQRT2 CSAWsimSQRT2B

For r = SQRT(3) below are the results from some simulations (for the Delta variant):    See:

COVID Odyssey: Winter Windup 7 ~ COVID-19 Delta Variant 2021 ~ Simulations

COVID Odyssey: Winter Windup 6 ~ COVID-19 Delta Variant 2021 ~ Does Ro = 12?

COVID Odyssey: Winter Windup 8 ~ COVID- 19 Delta Variant 2021 ~ Graphs

COVID Odyssey: Winter Windup 9 ~ COVID- 19 Delta Variant 2021 ~ Is Ro in the range 9 to 12.7?

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