Compelled vaccination would fall under implied power. Random fact of the day: ICE's jurisdiction is an implied power.
Here are the relevant parts of the constitution:
"Implied powers are which can reasonably be assumed to flow from express powers, though not explicitly mentioned. The legitimacy of these powers flows from the "General Welfare" clause in the Preamble, the "Necessary & Proper Clause", and the "Commerce Clause." " (Quote from Wikipedia)