New Member deadly allergic to cats

Asking this question for a new member: She moved into our small 17 unit townhome community which is self managed in August last year. Soon after her move-in, she was surprised to see random cats walking on her deck and yard. (Members own their building and the land property). She has a very serious cat allergy which has placed her in the hospital. This has happened twice and the hospital staff had a difficult time bringing the allergy under control - life threatening.
She asked me about the cats and I told her to take pictures and inform the Board of her serious situation. The cats belong to the adult child of one of the members, who lives with her mother. The Board spoke to the cat owner and explained the seriousness of letting their cats roam free and the impact it could have on the new member. The cats continue to roam and so with the Boards advice the new member called the police who spoke to the cat owners. Police said if it happens they will get a citation along with a fine.
If the new owner does have a potentially deadly allergic reaction, could she sue the Board? Could she sue the cat owners? all her communication to the Board is documented and now the police are involved. Police are in agreement that the local community rules protect her from having someone's cats being on her property. The HOA rules point out how to handle dogs; on leash, clean up etc, but no rules addressing cats.
Please provide your thoughts.

Do the covenants say anything about animals? Please quote exactly what the covenants say about any animal.

When you say "rules," what do you mean? Are these rules board-created? Or do you mean covenants?

If the owner documents carefully (with say film footage) cats on her property; this violates the covenants; and the board refuses to go after the cat's owner with say a warning and then a fine, yes, the board and HOA could be found liable for any damages (harm quantified in dollars) the women suffers.

The HOA should do exactly as it's doing. Ultimately, free-range pets are a city statute issue that the HOA's rules do not override. The HOA has no right to enter the violator's property to trap the cat and there should be no reasonable expectation that the HOA closely track a cat owner.

We've found foxes, coyotes, and great horned owls to be very helpful. Avian influenza is also showing promise.

Wendy, I think fines carry real teeth. Also I think the board's requiring the accuser to take video footage is a lot easier than getting Animal Control to trap a cat.

Sounds simple to me. Pass a regulation on free roaming pets, fine $100. Bet the $2 cats disappear.