Them finding the medicine prevented the disease spreading
Active and Passive Sentences
A sentence is written in active voice when the subject of the sentence performs the action in the sentence.
e.g. The girl was washing the cat.
A sentence is written in passive voice when the subject of the sentence has an action done to it by someone or something else.
e.g. The cat was being washed by the girl.
So - this could be put another way:
The disease was stopped from spreading by the using the medicine they found.