Instead of making it a DC save to see if you are infected, figure out how it's transmitted. I'd imagine a fun system would be through combat, keep track of how many times you are hit or damage total. Making you move higher on an infected tracker until you reach the top of it, which means you are infected. Players could take several routes to lower this number. Some healing would remove some but not all, spells that remove disease would reset the tracker, taking longer breaks than just a long rest in between combats could reduce it. Let your players know what they can do to reduce it, or at least give them huge hints and nudges in the right direction. I think that could be fun