this is a persistent effect, so it remains in place for the whole round until the turn comes back to you.
the travel ban immediately drops 1 level on the infection track
Incorrect. See my post above.
it drops 1 level with each player after you until the turn comes back to you and the card is discarded.
it wouldn't need to be a persistent effect card
It needs to be a persistent effect since it is reducing the infection ***rate***, not the current position of the infection syringe.