Alicia is being aggressively tickled by her older sister. which divisions of the nervous system are involved in processing the nerve signals

The tickling sensation activates the nerve endings, the receptors for touch in our skin that are part of the peripheral nervous system. The information about the sensation is then transferred through the nerve fibers to the central nervous system, the spinal chord, and the brain. The information is analyzed in the brain in the somatosensory region of the cerebral cortex and the cingulate cortex.
Therefore, both of the divisions of the nervous system, the peripheral (the nerves) and the central (the spinal chord and the brain) are involved in processing the tickling sensation.

Dna overload will occur