  The study of density-dependent stochastic population processes is important
from a historical perspective as well as from the perspective of a number of
existing and emerging applications today. In more recent applications of these
processes, it can be especially important to include time-varying parameters
for the rates that impact the density-dependent population structures and
behaviors. Under a mean-field scaling, we show that such density-dependent
stochastic population processes with time-varying behavior converge to a
corresponding dynamical system. We analogously establish that the optimal
control of such density-dependent stochastic population processes converges to
the optimal control of the limiting dynamical system. An analysis of both the
dynamical system and its optimal control renders various important mathematical
properties of interest.
