Not sure what exactly you're after. Any infectious disease is potentially a spreading one. As for creeping diseases, there must be several. Motor Neurone Disease could be considered to be one. There's Lou Gehrig's Disease, which is a bit similar. It does have a rather lengthy medical name. There must be a number of tropical diseases as well.
If this isn't much help, perhaps you can be a bit more specific
If this was a crossword clue, it would have been helpful if you had indicated how many letters, but no matter. I learnt a lot of things while I was delving around. Best of luck in whatever it is.