What exerts a centripetal force on a person running around a curve?

The inertial force of the body

Explanation:

Everybody that is moving in a curved path has an inertial force called centrifugal force.

The counterforce of the centrifugal force is called the centripetal force. It also acts on every rotating body.

This force is always directed towards the center of the origin of the curve.

The velocity of the object changes its direction and magnitude at any instant of time. But the speed and angular velocity of the object remains the same for uniform circular motion.

So, according to the Newtonian mechanics, it is the inertial force of the body responsible for the centripetal force.