Nope, I couldn't find a faq on gamefaqs and some other sites but it's not really surprising, these kind of games don't really get guides.
Maybe you could try playing it yourself and seeing if you can find out why the bears are getting sick? Unless it's one of those games with obscure reasons as to why things happen, it should be easy for an experienced gamer to find out what to do.
On the other hand there's always the possibility that somebody has played it over here and will chirp up. If not, try giving the game a quick look and looking for the most obvious answers (since it's a pet raising simulator) or googling.