My SIL in mid-stage of Alzheimer's refuses to bathe and barely cleans herself. Any advice?

My SIL has been living with us for several months. She is in what I believe would be termed mid-stage progression of Alzheimer's. She was always a stubborn person and the disease seems to have taken some of the most negative bits of her personality and multiplied them by 10. We understand where this comes from and do our best to let it slide, even when she says hurtful things to my wife. Before the disease, she was always proud of her appearance and enjoyed dressing up for a night out. Now that part of her has vanished. She has not bathed, showered or even washed her hair in 3 months. When we try to get her to do it, she either changes the subject, acts like she didn't hear us, or worse, gets violently agitated -- cursing and screaming at us. All she will do is what she calls "getting cleaned up." This consists of throwing some water on her face and rubbing it with a towel. Period. If it was just about her, we could deal with it. But her lack of hygiene is getting to a point where I think it could affect everyone in the house. She's developed this habit of grabbing a handful of tissues and going into the front of her pants, rubbing things off (because they itch, I think) and then just tossing the wad of tissues into the nearest trash receptacle. It doesn't seem to matter that anyone else is in the room. She is always playing with her false teeth, pulling them out, scraping off the Poligrip and reapplying more huge globs of the stuff. (She uses a large tube every 2-3 days.) Then she spends the time in between rubbing the film of dried denture cream off her hands, sprinkling it where ever it she stands. She never washes her hands -- no matter where they've been. There are wads of tissues everywhere, overflowing every trash can. (We go through as many as three boxes of face tissue a day.) She's even had a couple of Number 2 accidents and, after the most recent one, refused to bath. Needless to say, we've had to go behind here an clean things up where she's left "soil." I've got a pretty strong tummy, having seen the worst things that can happen to people in my former career. But I've gotten to where I'll chase after her when she heads to the kitchen to head her off before she handles any food. I absolutely do not want here to touch anything that may end up in mouth of anyone else. Frankly, I don't want her to touch anything at all, but that's not an option. I am genuinely concerned that she may pass some sort of nasty infectious bug to family and friends. We have grandkids and I really don't want them exposed to that. Top all that off with the fact she chain smokes 2 to 3 packs of cigarettes a day, so even the air is around here is pretty contaminated. (I run 2 air cleaners pretty much all day and night.) My wife is just as upset with all this as I am, but I think I'm the most vocal about it. Okay... I'm done ranting. Now, anyone, please, please, please offer any thoughts or advice you may have.