One of the patterns of growth described in The Lean Startup is the "viral engine of growth". This is actually already well studied in other fields, and there are dynamic models to simulate them. The SI model includes Succeptible and Infected individuals and the SIR model extends this with Recovered individuals. Obviously, in the case of a business, Infected = Customer / User!

If there is any interest I can prepare a short walk-through of how dynamic models work, and run through some scenarios of "epidemics".