COVID-19~ World-wide estimates. Is r^3 a good estimate for Ro?

We investigate if r^3 (r cubed) is a good estimate for Ro for COVID-19.

We have already looked at worldwide estimates for Ro if Ro ~ exp(2.5r – 2.5), where r is a daily increase in case numbers early in an outbreak. Ro is the average number of people one person may infect when there is no immunity in the community over a ten-day infectious period, and “exp” means “e to the power of” where e ~ 2.718281828 is a mathematical constant. See:

COVID-19~ Worldwide estimates if Ro ~ exp(2.5r – 2.5)

We look at the following two graphs:

Both graphs show use the same data:

r	exp(2.5r-2.5)	r^3  (1 d.p.)
1.0	1.00000	1.0
1.1	1.28403	1.3
1.2	1.64872	1.7
1.3	2.11700	2.2
1.4	2.71828	2.7
1.5	3.49034	3.4
1.6	4.48169	4.1
1.7	5.75460	4.9
1.8	7.38906	5.8
1.9	9.48774	6.9
2.0	12.18249	8.0

We see that for r up to around 1.5, r^3 provides a good approximation for Ro.

These vales for r contain all but the three highest countries is the table below for the original 2020 outbreak of COVID-19.

This PDF contains more countries:
COVIDWorldAllCasesEXP

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