It wouldn't need to be an epidemic, just an illness one caught from the other or maybe they were both injured in an accident. This is an age before preventive medicine and even diarrhoea which is controlled now, could severely dehydrate someone.
Or they could have died of unrelated causes. I have instances of family members dying within a few days of eachother from different illnesses.
Unless it says in the burial register I guess you are unlikely to find out.