we used to have this problem although not as bad as yours sounds, the only way is to mix a strong weed killer with wallpaper paste and using a glove smear the resulting thick gel over the whole stem ( this could take some time ) but is worth it in the long run, since there are no proper leaves the ordinary thin stuff just runs off, it also has black or dark brown roots that help it to spread, and as if thats not enough every second year it puts out pencil like 'fingers' that i beleave could be its flowers, so treat these as well if you see any, it worked for us, mix the stuff in the open air in case of fumes, and good luck.