We look at formulae for calculating Ro based on Re case numbers. See image below. For background see the bottom of this post.
To[i] be the total number of case numbers for Day i without isolation (i = 1 to 10).
Co[i] be the number of cases for Day i without isolation.
ro be the daily increase without isolation.
Ro be the average number of people one person may infect on average over a ten day period without isolation.
Similarly we define Te[i], Ce[i], re, and Re to be the effective numbers with isolation.
Where there is no confusion, we refer to ro and re simply as r.
The cases Ce[i] are isolated when they are discovered.
To calculate Ro, we need to include their spread as if they had not been isolated.
Ce = 10
Te = 10
For i = 1, 2, …, 10
Te[i] = re x Te[i-1]
Ce[i] = Te[i]-Te[i-1]
To = Te
To = Te + Ce
For i = 2, … , 10
To[i] = To[i-1] x re + Ce[i-1] x (re – 1)
ro = (To / To ) ^ (1/9)
We calculate Ro and Re from our formula. See top of image below or:
This PDF may be easier to read:
For background see: