If you lift your heel off the ground while keeping your toes on the ground...and then the "vibrating is more prominent", then you have a condition known as Clonus, which is usually a red flag for some kind of neurological issue. For me it was mild pressure on the spinal cord from a whiplash injury. If that's what is not happening, I 'm not sure what you're referring to.
It could be due to some sort of nerve entrapment/compression. Might be in your foot somewhere or even in your spine. I've have spine problems and with my last bout of left sided sciatica, after a few weeks, I noticed I was getting a buzzing sensation in my right foot on the bottom, just below my big toe. This only happened when I leaned my head forward. I was told this can happen b/c when when you bend forward, it stretches the dura matter (a covering over the spinal canal) and if you have compression in there, it can cause parasthesias (shock feelings, stabbing pains, pins & needles, buzzing, vibrating, etc..). This is not to say you have this, but it's a possibility. ANd even so, doesnt mean it's serious or not easily treatable. It might even be swelling or nerve impingement in your foot somewhere from from the running. There are other reasons also, but certainly dont start thinking the worst. If it's been going on for a while and is really bothering you, then you should see a doctor to check into it.