Don't kill all the frogs! Keep at least 2 around so Villagers will get sick. Your healer-in-training can then heal them and advance faster. You can have an adult catch a frog. They will get sick about 1/2 the times you try this, but then frog is gone and you have to wait for a new one. Otherwise, just let a few frogs roam the island and a few villagers eventually get sick.