I get that, I am trying to understand the math and model behind this. Let me clarify the paradox: Say Ebola has a R_0=4. That means one person infects 4 people

I get that, I am trying to understand the math and model behind this. Let me clarify the paradox: Say Ebola has a R_0=4. That means one person infects 4 people under some circumstances. It doesn't matter if Ebola kills someone in 3 weeks or in 5 seconds, under some circumstances one person must be infecting 4. What are those circumstances, and how are they different from the actual circumstances which led to the Ebola epidemic stopping.