How did people control the spread of disease before epidemiology? Is it possible for people in the near tropical parts (like the Basilisk or Summer Isles) of ASOIAF to better their chances of staying healthy?

Before the modern science of epidemiology, you still had a general understanding that quarantining sick people or towns, etc. was a good idea. Such quarantines were not that effective, due to a lack of state capacity to enforce them and a lack of understanding about what the potential vectors for infection were, but they were better than nothing.