When I was just 21 and freshly out of the service, I solo hiked the Pacific Crest Trail from Donner Summit to Bishop California. I went slow and it took 23 days. I wanted to look and see the sights instead of just bore on from one point to the other.
At first I was really paranoid about meeting other folks on the trail as well as animals bigger than me.
About the third day on the treail I adopted a mindset that I was the predator. I'd look ahead for other hikers and upon seeing them I'd step behind a tree or rock and as they passed, I'd step out and scare the crap out of them.
I found that this tactic helped me overcome my uneasyness of being alone on the trail. I had just finished reading Steppenwolf by Hermann Hesse and that inspired me to be the "Predator". Sounds silly now, but it really helped.