Hi!
This is a great looking app! It seems to do its job, but it is a bit slow for me. I'll second nirgrahamuk's recommendation!
Additionally, here are some quick ideas:
(1) when I add a new country, are you re-rendering the entire plot? Instead, you might consider just adding an extra layer onto an existing plot. Same for other features--is there anywhere where you can re-use parts of an already-existing graph or dataset?
(2) Maybe a button to refresh the graph would be good? If I change a bunch of parameters, I don't want to see the intermediates--I'd rather just change all of them and click a button when I'm ready.
(3) For aesthetics--shinycssloaders may make me more patient?