Odds of Getting In
Being an epidemiologist takes a lot of book work and a ton of school time, so competition for jobs is slimmer than, say, it might be for a barista. And it's not like you can just breeze through the course load. Getting into the right programs requires solid GPAs and a ridiculous amount of effort. Fortunately, hiring bodies know that, and so when you show up smart and shiny out of grad school, they're typically thankful to have you.
So, is it easy to get in? It is if you did the work to get there. Now, whether or not you consider that part to be easy is on you.