I always use research and statistics as directional, baseline, info. It's very helpful; humans are for the large part, quite predictable. I always use the example that a LE friend of mine gave me once. "How many women have jewelry/valuables "hidden" in their underware drawer right now? That's the *first* place a burglar looks!"
I was imagining in my mind how this crime unfolded, and here's the scenario/profile I came up with. Several gaps in the theory, but a place to start.
The Perp is in late teens, maybe very early 20's, but most likely around 19 years old. Lives at home, not in school and has very spotty work history. A problem child. May have displayed developmental issues, most especially impulse control. History of animal abuse, lacks empathy. If there is a younger sibling, history of being abusive to them. Fascination with fire, perhaps noted for setting small fires. May be history of mental illness of some sort on mothers side of family. History of bedwetting beyond average age of cessation.
The Perp lives within "observation" range of the victim. Tracked her every move; knew her routine very well. He might have known her indirectly, such as bagging her groceries, or setting up scenarios where he would be in close proximity to her. The day of the murder was well planned. For some reason that I can't quite figure out, I really do not believe he escaped via a car. I think his incendiary gear was either in a backpack, or stashed somewhere. He grew up in the area, so knew his route well.
The Perp lay in wait, and had the advantage of the element of surprise. I think he attacked her from behind. Do we know if she sustained a blow to the back of her skull? He dragged her off her jogging path, stunned, in to the area where she passed over. Hidden from view. He took objects to nourish his memories of the attack. As far as the use of fire, in my amateur profile, this gear was obtained from a gas station where repairs are made to cars, or an auto repair/body shop. He either stole the gear, has access to it; maybe his father works there?
When the crime was reported to the public, his family immediately thought of him. They know he is unstable. I don't think this really had much to do personally with the victim; I think she was just "prey" who was in his target zone, his geography. She was an object to him, not a person. No empathy. (Obviously). I don't see this as personalized towards her, just fulfillment of his aberrant mind.
I also believe while devious and furtive, he will absolutely be arrested. His behavior is impossible to completely conceal, and I believe his family knows this.
So this is my *amateur* profile of this Perp. Emphasis on amateur. We will see how close I am when he is arrested. And he will be, and soon I believe.