Cupcake has an obsession with bugs, mostly flies. She chases them around the house, but sometimes she actually manages to kill one and eat it. Before I thought that she used to just play with them but today I saw her catch one under her paws and eat it, afterwards she licked her lips. I also noticed that she can scoop dead flies between the window panes. I don't want her to catch a disease by eating them, like cats can from rats. Are flies dangerous and do they carry diseases?