1. A wakefulness level estimation apparatus, comprising: an ECU having: an estimation portion operable to estimate a level of wakefulness of a subject person based on one of a wakefulness level estimation function, of which a variable is a wakefulness level correlation value of the subject person, and a difference between the wakefulness level correlation value of the subject person and a reference value of the wakefulness level correlation value; a stimulation detection portion operable to detect whether an awakening stimulation is externally applied to the subject person and operable to detect that the stimulation is externally applied to the subject person when a vehicle runs in an area in which an awakening effect is produced by the stimulation being externally applied to the subject person, the area being one of (i) an area in which a facility is provided on a road to produce the awakening effect on the subject person, (ii) an area in which a tension stimulus is applied to the subject person due to a change of road circumstances and surrounding circumstances of the vehicle, and (iii) an area in which a physical stimulus that produces the awakening effect is applied to the subject person; and a correction portion that, when the stimulation detection portion detects that the awakening stimulation is applied to the subject person, is operable to compare a level of wakefulness of the subject person estimated by the estimation portion after the simulation detection portion detects that the awakening stimulation is externally applied to the subject person with a level of wakefulness of the subject person estimated by the estimation portion before the stimulation detection portion detects that the awakening stimulation is externally applied to the subject person, and is operable to repeatedly perform a correction of one of the reference value of the wakefulness level correlation value and the wakefulness level estimation function, which is used for estimating the level of wakefulness of the subject person based on result of comparison of the level of wakefulness after the stimulation and the level of wakefulness before the stimulation, so as to make the level of wakefulness after the stimulation higher than the level of wakefulness before the stimulation.