Network Epidemic Control via Model Predictive Control: Extended Version
Abstract
Balancing the societal costs of non-pharmaceutical interventions with epidemic suppression requires adaptive feedback control. Rather than relying on state-dependent operational caps, we formulate an infinite-horizon optimal control problem for a networked SIQR model that strictly enforces suppression via a hard spectral constraint on the transmission dynamics. We derive a safety-critical Model Predictive Control (MPC) approximation that embeds this spectral certificate stage-wise, yielding a tunable exponential decay rate. Furthermore, we construct a terminal set ensuring recursive feasibility and a feasible continuation that decays globally, proving positive invariance directly via the physical depletion of susceptibles rather than standard quadratic Lyapunov functions. To handle prediction uncertainty, we develop a robust counterpart that replaces nominal constraints by upper-envelope versions, recovering recursive feasibility and finite-horizon realized decay. We conclude by validating our approaches using simulation studies that leverage public data from counties in the state of Massachusetts.
Cite
@article{arxiv.2604.13357,
title = {Network Epidemic Control via Model Predictive Control: Extended Version},
author = {Mahtab Talaei and Alex Olshevsky and Laura F. White and Ioannis Ch. Paschalidis},
journal= {arXiv preprint arXiv:2604.13357},
year = {2026}
}