AIO?

I'm in Florida. German Roaches are appearing randomly in places with no food access. My partner thinks it's our down stairs neighbor causing the issue he uses his back patio like a place to hold his garbage instead of throwing it away (we can look down between the back patio wood boards and see his trash and his 50 gallon storage bin filled with rain water, trash and red cups)

whenever our property manager does first of the month inspections she sometimes brings pest control and he doesn't really spray he hits one corner and around the fridge and walks out.

The property manager says I'm the only one who complains about the roaches.. so they have to make special requests to spray our particular building. I don't really want to keep staying here because I know how bad they can get.

She doesn't look at his patio or any other the apartment patios her main concern is in the inside interior.

I would like to break the lease because of it. My partner's family thinks I'm overreacting about breaking the lease because it's the south no apartment is roach free?