I think it's going too far to say that the Romans understood disease
What does "understood disease" mean?
If the Romans knew that setting up an army camp one way leads to half the soldiers unable to step away from the latrines and setting up the camp another way leads to most everyone being fine -- does that imply understanding disease?
And, by the way, I wonder if a big factor in comparing Roman to medieval European armies would be the prevailing military strategy. In Roman times warfare was mostly mobile -- armies marched, then fought. In medieval times a lot more focus was on sieges where an army stays in one place for a long time. Obviously a marching army is less vulnerable to disease than an army that camps in a single place for months.
Sure, but I think it is going too far even to say that the Romans thought that latrines reduced disease. Do you have ancient sources suggesting otherwise?
Yes, the more mobile the Romans are the less the design of their camps matters. And yet, they got it right and the medievals who needed it got it wrong.
Related: Son of Low Hanging Fruit, Low Hanging Poop
A post by Gregory Cochran's and Henry Harpending's blog West Hunter.