Go to furniture upholsterer or an upholstery supply & buy some 2" wide 'elastic' banding. It's what those furniture guys use for springs in antique furniture.
Pull the covers & the foam. Wrap the elastic from side to side & then front to back, weaving the elastic over & under each wrap in the opposing direction.
You can do each run across individually or in one piece.
I prefer the latter, but if doing in one piece wrap once around the frame once between each run. This will help to prevent the elastic from moving & bunching up on itself.
The elastic doesn't have to be really tight. Just snug enough that the elastic is under some tension. The weaving of the elastic will make it stiffer with each run. Too tight & every time you sit on the seat, it will over-stretch & break down sooner than it should.
This makes for a very comfortable seat.
The ends will have to attached to itself at the beginning & the ends if doing continuous, or on each run across/front-to-back. I use 'hog-rings' for that. Need special hog-ring pliers for those. You can get the pliers & enough h/rings from the upholstery guy or the supplier for under $20.00. Figure $30-$40.00 for the elastic.