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FROM A PAPER BY by John Holland Jones at Stanford University:

https://web.stanford.edu/~jhj1/teachingdocs/Jones-on-R0.pdf

If we look at that mathematically, this comes down to three factors.

These three factors are:

1. transmissibility — the number of infections per contact, or (infections/contact), which we’ll call t

2. contact — how many contacts there are on average between an infected individual and susceptible individuals over time. So (contacts/time), which we’ll call c.

3. duration — how long someone who has become infected remains able to transmit the virus. So this is (time/infection) and we’ll call that d.

The number of new cases, R0, is proportionate to the transmissibility, times the number of contacts during the time it’s transmissible, times the length of time it is transmissible.

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For the mathematically inclined:

R0 ∝ t × c × d

None of these three numbers are things we can directly measure, especially in the course of an epidemic spread, but we can take other information and estimate it using models. The key point here is that R0 by definition represents the number of new cases following an individual case.

That turns the progress of an epidemic into a familiar equation:

number of new cases = number of starting cases × R0n

where n is the number of "generations".

If that doesn't look familiar, look at your credit card bill. It's the same way interest is calculated — (1+r)n. R0 here is just principle and interest.