We perform simulations of the three-dimensional frustrated anisotropic XY model with point disorder as a model of a type-II superconductor with quenched point pinning in a magnetic field and a weak applied current. Using resistively shunted junction dynamics, we find a critical current Ic that separates a creep region with immeasurably low voltage from a region with a voltage V∝(I−Ic) and also identify the mechanism behind this behavior. It also turns out that data at fixed disorder strength may be collapsed by plotting V versus TI, where T is the temperature, though the reason for this behavior as yet not is fully understood.