Joel-Miller-Lab / InfectiousMath

This is intended to provide a set of self-contained examples, much like the Mudd math fun facts which demonstrate mathematics through biological examples.
MIT License
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Geometric Series #3

Open joelmiller opened 2 years ago

joelmiller commented 2 years ago

Assume we infect 1 person. How many infections occur within 'g' generations, assuming that the expected number of transmissions is R_0?

1 + R_0 + R_0^2 + ... + R_0^g = [1-R_0^{g+1}]/[1-R_0]

[need to add discussion about why successive generations are just R_0^n]

If R_0<0 what is the limit as g -> infinity?

1/[1-R_0]