Medical waste in my yard, constantly

I live behind a nursing home, been here for 5+ years. We’ve had issues with their waste ending up in our yard the entire time. It’s mostly harmless little things, but the latex gloves really gross me out. I’ve talked to the city about it (told me they can only reprimand them when it’s overflowing) and tried to contact the nursing home directly and had zero luck getting them to manage their trash better. The dumpsters are usually open and often overflowing.

Looking for suggestions on how to get this taken more seriously because I’m so sick of it.