How to clean the dust brush than came w/a dust pan?

Use the highest setting on your hose.

Hello, you should be able to pre-soak it with simple green r another cleaner like Mr Clean, use it undiluted then rinse it with hot water until the water runs clear, clean the dustpan too, let dry and should look way better!

Is the handle plastic? I would soak and agitate in in a bucket of soapy water , then rinse and airdry.

I agree with Debker, use something that will fight the sticky stuff it has gotten into, even Dawn dishwashing liquid to get rid of all the gunk stuck on the bristles. Work it in good with your hands and let sit for a few minutes, then rinse well. If you want to soak it afterwards to make sure it is clean, do so. Once you rinse it, douse it with vinegar to make sure you have all the soap out and let it dry. The vinegar will also disinfect it , just incase it all didn't come off.

When I get enough tools, I wash hair brushes, dust brushes etc all in the dishwasher (no dishes of course) and run a load! also nick knacks etc , anything not eaten out of to wash and make a full load. Most nylon brooms can come unscrewed from the handles to make them fit in the dish washer

Soak in oxyclean let dry

These bristles are so tightly intertwined and made more so by strings and other remnants of debris that I would probably just buy a new one. I mean one or two a lifetime isn't bad! Compared to a cost of a refrigerator or other appliance!

Soak in a bucket with your favorite household cleaner for a few hours. Rinse outside with a garden hose.