How to Keep House Clean in Tucson

I'm fairly new to Tucson (and Arizona in general) still, and I'm struggling to keep my house clean since it gets dirty (especially dusty) again so quickly after cleaning. For example, I will sweep and mop the whole house then a day later (or less), dust/dirt and little leaves will appear all over the floor again. Is this normal or is there something special I should be doing in this desert climate to keep the dust away for longer than a day? My house getting dirty again so quickly after cleaning it is driving me nuts.

For some background: I live in a single-story, older house with all tile floors as well as a yard, dog door, and a small dog. I bathe my dog regularly. The yard doesn't have gravel (yet) but is au naturale at the moment with a few small Mesquite trees and catcus. I've replaced house air filters often and have multiple portable air filters running constantly. I have a no shoes inside policy. Am I missing something? Is there something else I should be doing?