Tumors in African Soft Furred Rats

I have been breeding African soft furred rats for a couple years now. I find them to be less smelly than Norway rats, and they are prolific breeders....
However, in addition to being nasty biters (ouch) they are prone to developing nasty rapid growing tumors. Within a week an affected rat can go from having rough-looking fur (tumors developing underneath) or a sore on the eye, ear, or under the jaw; to numerous bumpy, sometimes bleeding, lumps all over their body. I did a bit of research and found a bit more info on this problem:
http://www.metalmonkeyexotics.com/blog/?page_id=333

"Tumors

"ASF's are prone to spontaneous, fast growing warty tumors. From my readings in various papers, the warty and ulcer like tumors known as keratoacanthomas and squamous carcinomas, are associated with a papillomavirus (MnPV). The tumors can be seen in the vaginal region as a clustered mass, along the tail as bumps, on the back and hind quarters as warty black growths, or on the face of the animal. (Pictures can be found here)

"They will develop warty tumors, patchy hairloss, and osteoarthritis as they age past approx 9 months, although it can be younger, or delayed as much as 14 months, or not at all.

"So far, it would seem that the tumors develop after 9 -12months of age, although not all will get this condition.I have at least one Amber colored female well over 14 months of age that still has not developed any skin tumors or growths.

"The tumor development can be very fast and spontaneous. I've had one female just recently (6/1) who within days developed fast growing tumors all over her body, under the skin and on the skin surface. I should have taken a picture, but I didn't remember to before she was euthanized and destroyed. It was disturbing to see the alarming rate that the tumors grew, she had just reached approximately 8-9 months of age when these tumors developed."

Though I try to cull affected animals as soon as I notice them, I haven't been able to make a noticeable improvement since I have a colony-style environment. I am seriously thinking about trying to do some strict selective breeding to see if this problem could be at least reduced or delayed if not irradiated (I could work on the aggressiveness and biting too) .
Also, ... is there something in captivity that is causing this? Are they missing something in their diet? Do they need a different bedding? Do they need some light exposure?
I need to do more research. ....