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The optimal control of epidemic-like stochastic processes is important bothhistorically and for emerging applications today, where it can be especiallyimportant to include time-varying parameters that impact viral epidemic-likepropagation. We connect the control of such stochastic processes withtime-varying behavior to the stochastic shortest path problem and obtainsolutions for various cost functions. Then, under a mean-field scaling, thisgeneral class of stochastic processes is shown to converge to a correspondingdynamical system. We analogously establish that the optimal control of thisclass of processes converges to the optimal control of the limiting dynamicalsystem. Consequently, we study the optimal control of the dynamical systemwhere the comparison of both controlled systems renders various importantmathematical properties of interest.

Control of Time-Varying Epidemic-Like Stochastic Processes and Their Mean-Field Limits