  We study the force that non-interacting point-like active particles apply to
a symmetric inert object in the presence of a gradient of activity and particle
sources and sinks. We consider two simple patterns of sources and sinks that
are common in biological systems. We analytically solve a one dimensional model
designed to emulate higher dimensional systems, and study a two dimensional
model by numerical simulations. We specify when the particle flux due to the
creation and annihilation of particles can act to smooth the density profile
that is induced by a gradient in the velocity of the active particles, and find
the net resultant force due to both the gradient in activity and the particle
flux. These results are compared qualitatively to observations of nuclear
motion inside the oocyte, that is driven by a gradient in activity of
actin-coated vesicles.
