COVID Odyssey: NZ New Year Fear 17 Post #944~ COVID-19: Calculating Ro based on Re Case numbers

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.

We obtain:

Ce[0] = 10

Te[0] = 10

For i = 1, 2, …, 10

Te[i] = re x Te[i-1]

Ce[i] = Te[i]-Te[i-1]


To[0] = Te[0]

To[1] = Te[1] + Ce[1]

For i = 2, … , 10


To[i] = To[i-1] x re + Ce[i-1] x (re – 1)

We estimate

ro = (To[10] / To[1] ) ^ (1/9)

We calculate Ro and Re from our formula. See top of image below or:


We obtain:


This PDF may be easier to read:

For background see:


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