Interlude told them that they did indeed have a cure, but it was located further north, in yet another secure location. Monsters roamed the roads between there and here. The only ones that would be able to deal with it were the survivors. Interlude gave them a van, a gun each, their medication, and enough money for fuel. If they made it there, whoever was still alive could take the cure.
They are fighting a war not only against monsters, but against their own bodies.
Important Information Regarding The Trip:
Interlude estimated that the trip would take ten days to two weeks.
They have enough medication to last three weeks, just in case.
They have an Interlude card that allows them to get as much food and gas as they need.
They also have emergency medication, in case one of them deteriorates rapidly and needs to be stabilised.
That^
Is part of the intro post. So I doubt they'll run out of medicine.