i have something similar and used zip ties. our run is entirely hardware cloth, except for under the shade cloth, that i used the chicken wire we already had on hand, folded off center so the spaces are smaller, secured in place and put the tarp over top. for the apron i used more hardware cloth, zip tied to the run itself and used landscaping staples hammered into the ground to secure, covered in landscape cloth and mulch.
check your seams periodically, sometimes the plastic ties will loosen slightly or get damaged by severe weather fluctuations. but overall, if you don't have wood to attach your screen by, its the simplest solution. we used the metal zip ties at stress points and heavy duty plastic for the rest.
