How do I get rid of brown dust?

Have you had your air ducts cleaned? That's the biggest cause of dust. Do you leave your windows open? That too is a big contributer of dust.

check filter on ac heat unit

Where is the brown dust? Where do you live? Is it sand?

Hi ! Where are you finding this dust ... Could it be from termites ? If your Windows are open and you live in a dry climate of have a lot of dirt in your yard , it could be coming in from the outside .

Have your duct work cleaned. Seal all windows and doors, if you can see light then dust can get in. Damp dusting will also help.

Damp dusting is the answer. I live where it is very very dusty. Make sure you clean or replace your HVAC filters monthly. Also clean screens at least twice a year if you have the doors and windows open like I do.

https://www.epa.gov/indoor-air-quality-iaq/should-you-have-air-ducts-your-home-cleaned#Does

https://todayshomeowner.com/hvac-duct-cleaning-scam-or-worth-it/