Epidemiology for Toddlers

Savvy still calls chicken pox, picken chox. While she can't get the name right, she's doing some clever digging into epidemiology:

Sav: Who gave me picken chox?

Mom: Your friend, William.

Sav: Who gave him picken chox?

Mom: I think it was one of his friends at nursery.

Sav: And who gave it to them?

Mom: I am not sure.

Sav: What would happen if no one in the whole world had it to pass on?

Mom: ??? (Would it die out or live dormant and resurface???)

Sav: What if we had medicine to make sure no one could catch it? Then who would be the last to have it?

And on, and on, and on...