Do Rats Carry Disease?
I am worried that rats carry diseases. I clean and disinfect my pet rats' cage once a week but sawdust sometimes escapes from the cages which is contaminated with urine. Have I placed my other pets (cats and dogs) at risk?
Wild rats carry diseases to which both humans and animals are susceptible. Since yours probably come from a line which has never had contact with wild rats, it is highly unlikely that they carry any more disease risk than, say, a hamster.
The vaccines that your dogs and cats should get annually will protect against the diseases your rat may carry (such as leptospirosis).