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arXiv · 1709.10345

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

Yingdong Lu·Mark S. Squillante·Chai Wah Wu
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Abstract

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.

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Yingdong Lu, Mark S. Squillante, Chai Wah Wu. 2017-09-27. Control of Time-Varying Epidemic-Like Stochastic Processes and Their Mean-Field Limits. https://arxiv.org/abs/1709.10345

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