According to the Dutch ministry of health there's no reason whatsoever to keep your cats inside in order to prevent the spread of H5N1. There's hardly any chance of them getting infected anyway.
According to Dr. Kuiken (which translates as Dr. 'Chick') and Dr. Rimmelzwaan (which translates as Dr. Swan - I am not making this up), the risk is definitely there. And Nature seems to think so as well.
Fortunately, Ender is much too busy sleeping anyway.