Plague

[Aemilius Paulus]

They can be a devastating weapon if used correctly, savaging enemy populations and ruining their potential to build armies.

They would be, if not for the fact that a certain part of the EB script gives back almost all of the population every time AI recruits anything... As they say, AI has the script and you have the brains...

Anyone know if building loads of health buildings help prevent it?

Actually this is one of the few times when such trigger is present. Yes, plagues happen when a city is full of squalor and lacking public health. The trigger is started by this. To counteract it, just build the public health buildings and all will be fine. The only problem is that plagues can appear almost everywhere (quite a large number of provinces are marked as plague-prone in EB) at any time...