Without wishing to interfere,

I wanted to say something (and you can imagine how busy Chickenvet gets - so just in case....)
Rats are really bad news for chickens - it is essential to keep on top of numbers or they will suddenly multiply like mad. With chicken feed around and fresh water they will thrive so agree totally with CV on the Rats...
Good general housekeeping is basicly what I would be thinking of - firstly with the rats and then an ongoing program of keeping the birds clean. There are diseases all around but I have found over the years that a good strong immune system (ie healthy birds) through a good diet will keep most problems away.
'Secondary' infection is basically when a bird becomes ill with one thing which causes them to pick up something else that's passing.
I quote from Chickenvets
Respiritory Disease in Chickens article:
"....are mostly viruses which will not respond to antibiotics. However these viruses often damage the respiratory system sufficiently to allow secondary bacteria such as E. coli and Pasteurella to cause infection and in severe cases blood poisoning."
So by keeping the chooks fit and healthy and not allowing one disease to take hold, you are stopping another! Bingo
I don't know much about Rabbits - but if there was a possibility of Rats getting in somewhere (they can squeeze through very small holes) this might explain it??