Applied math is very broad. Your post shows me that you think that a PhD in applied math is a very specific thing and that PhD's in applied math know roughly the same things. This is of course false. A PhD in applied math is a title that is used, but is rather meaningless other than that it says that you have applied math somewhere.
You could and should be more specific. You are interested in epidemiology? Well, then you should do research in epidemiology. Find yourself a good advisor in epidemiology. Whether this advisor is in the math department or another department depends on your tastes. If you like the underlying mathematical aspects of it, then somebody in the math department would be suitable.
So instead of a vague thing like "applied mathematics", try to find out what exactly you're interested in and in what aspect of the theory you would like to do research in. Then you should see which people do these kind of research and to what department these people usually belong.