Seal Up Those Rat Holes
Many, many times exterminators are paid by the call, that is each time they go out and bait/lay traps someone writes a check. With that incentive, some are rather lax in doing the job correctly. Why should they? Once the rats are gone, so is their meal ticket. If you are catching several large rodents, you have a PROBLEM, and unless the thing is dealt with firmly,it will only get worse. Remember those cartoons where the rats/mice tie up the lady of the house and dance around like Indians? *LOL*
May not be an expert on rodents/rats, but live in a city where the things are EVERYWHERE, and were recently featured running amuck in a fast food restaurant, so think I know one or two things. Any exterminator have ever known says the same thing: one must first seal off all points of entry, then remove all food sources, finally bait/trap.
If there is a entry way from the sewer/your basement into the building, think of it as rat highway. You'll keep trapping them, but more will keep coming. They follow the scent of previous rats that have gone before them.
By all means call your local board of health ASAP, and also (funds permitting), contact another exterminator and ask to have your apartment/home rodent proofed and checked for where the buggers are coming from. If you are not too delicate, you can rodent proof your home yourself, but it must be a through job. Everything must be pulled out of/away from walls, cabinets and any holes larger than a dime must be stuffed with the most coarse steel wool (adding some crushed glass is good), and packed TIGHT. This includes areas behind the range, and behind/under the fridge, around all steam/heat/water pipes, electrical outlets.
Speaking of the fast food restaurant rat show, every building around that restaurant called in top shelf exterminators to have everything locked and loaded against rats moving house into their buildings once the extermination program was underway.