Probably bacterial, just because darkening and death of plant parts often is. And this is a tropical plant that can get that kind of thing in cool and damp climates.

Will a fungal spray help then? Copper?

Find out what the problem is before spraying. If you have the ability to ask at a local Cooperative Extension office, take your plant there and see what they say. Find the location on the internet by searching with the name of your state followed by "extension".