OMG! This is a horrible situation. Thank God you care!
I can tell you from being an experienced rescuer for many years that a trap will probably not work and rarely does. Stray dogs are very smart and very cautious. My sense is that he/she will steer clear of it even with a steak inside. My partner years ago suggested we try a trap for a dog we knew ran off 6 months prior from a vet tech while being spayed. I spotted her one day when I changed my directions home and went a different way! Wierd! She ended up across a major highway hanging out in a neighborhood. We found out thru talking there was a woman who somewhat befriended the dog in the area she was hanging around in. She would feed the dog and leave a blanket in the garage where the dog would sleep at night. She could never get close to the dog. Long story short, she closed the door on the dog one morning and we contacted the owner and she got her dog back.
Now this was a dog who had an owner for a few weeks before the spay and she did not trust anyone nor would she let anyone get within any short close distance of her.
You will have to befriend this dog with constant food and treats and maybe leave the food in a garage, a big space where he/she can eventually be closed off in after he/she has been in and out quite a few times and feels safe in the area. It also has to be a very quiet area. No kids screaming or loud noises and voices. It takes alot of patience but the dog can and will be caught!
Hope this helped and sorry for going on and on! Good luck!
If you do want to try a trap make sure it is in a really quiet area where there are no people around, like in the bushes somewhere. It is worth a shot! He may be the one to go in! Good luck!