Benchmarking Optimal Control for Network Dynamic Systems with Plausible Epidemic Models

ABSTRACT

The sheer dimension of network dynamic systems adds a challenge of scale to synthesizing optimal control, which the techniques such as mean-field approximation, reinforcement learning, and graphon mean field games attempt to overcome. We propose to use compartmental metapopulation epidemic models derived from open data to benchmark these advanced approaches on an important problem with intuitive visualization options such as choropleth maps. To this end, we formalize a procedure for generating plausible instances of such models with 1–64,735 nodes based on open census data for the contiguous U.S., each with a network of daily commute and airplane travel, coupled with a formal aggregation routine enabling a view of the same geography at different resolutions, illustrated by merging the 2,072 census tracts in Oregon and Washington states, together with their travel networks, into 75 county-level nodes, 23 “airport service area” nodes, and 2 nodes for states themselves. These four cases, and ten other, are then put through 180-day “patient zero” scenarios in a Metapopulation SIR Model with per-node “lockdown level” control, with the objective of minimizing the cumulative number of infections and the lockdown level. The optimal control is derived through the Pontryagin Maximum Principle and numerically computed with the forward-backward sweep method. To ensure reproducibility, the instance generator, solver, and visualization routines are available at https//github.com/yvs314/epi-net-m. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.