  The optimal control of epidemic-like stochastic processes is important both
historically and for emerging applications today, where it can be especially
important to include time-varying parameters that impact viral epidemic-like
propagation. We connect the control of such stochastic processes with
time-varying behavior to the stochastic shortest path problem and obtain
solutions for various cost functions. Then, under a mean-field scaling, this
general class of stochastic processes is shown to converge to a corresponding
dynamical system. We analogously establish that the optimal control of this
class of processes converges to the optimal control of the limiting dynamical
system. Consequently, we study the optimal control of the dynamical system
where the comparison of both controlled systems renders various important
mathematical properties of interest.
