Hi M.,
We had roof rats a few years ago, and at least one got into our attic. That was too close for me, so we called a specialist pest control company.
It was probably more than one looking at the pictures of the damage, but after the company completed the intial steps, only one remained in the attic, and that one was the one they caught.
I found Terminex and Orkin to be utterly useless in our case. Go to your yellow pages or look on-line for a company in your area that specializes in removal of pests like rats, mice, and pigeons. There should be quite a few as roof rats and rats, in general, are not uncommon in your area.
These specialists do a process of exclusion, which means they examine your attic, home, whatever to identify sources of entry, and then they install the proper barriers to prevent re-entry. Then, and only then, should traps and/or poisons be used. It makes no sense to get rid of the ones you have if you don't take away the entry point for the rest of the pack or future pests.
Please remember that it isn't enough to get rid of the one(s) you have. You *have* to block off all access routes, which isn't always easy to determine by yourself, and you must make your premises inhospitable to pests by removing water, food, and shelter sources for them. (All garbage and pet food stored in garages should be sealed in airtight containers. Do not leave pet food and water bowls outside or in garages).
Good luck with this! I do know how horrible this can be. Message me if you want more information or if I can be of any further help.
J. F.
ETA: You're getting several responses suggesting the use of poison. I just want to urge you to use caution if you do this on your own. If you have very small children or pets, the use of poison should really be restricted to professional use as these companies use locked, tamper-resistant containers or boxes so that children and pets cannot easily get into them. I have no ties or loyalties to any particular company, by the way. It's just that these poisons are so lethal that extreme caution is necessary when using them.
Even though it has been almost 4 years since our problem, I still have the company keep the boxes hidden around the perimeter of our house and yard. They come once a month to check the bait stations and change the baits, if necessary. There hasn't been any real activity in a long time, so I was thinking about canceling the service, but after reading your post and recalling that mess, it's worth the peace of mind to keep it.
I hope you get this solved quickly!