Network Epidemic Control via Model Predictive Control

TL;DR

This paper develops a Model Predictive Control framework for epidemic management on networks, balancing societal costs and infection suppression, with proven stability and robustness.

Contribution

It introduces a spectral decay-based MPC approach for epidemic control that guarantees stability and robustness in a networked SIQR model.

Findings

MPC maintains exponential decay of infections during surges.

Reactive control fails under surge conditions, MPC succeeds.

The approach reduces societal isolation burden compared to myopic control.

Abstract

Non-pharmaceutical interventions are critical for epidemic suppression but impose substantial societal costs, motivating feedback control policies that adapt to time-varying transmission. We formulate an infinite-horizon optimal control problem for a mobility-coupled networked SIQR epidemic model that minimizes isolation burden while enforcing epidemic suppression through a spectral decay condition. From this formulation, we derive a safety-critical Model Predictive Control (MPC) framework in which the spectral certificate is imposed as a hard stage-wise constraint, yielding a tunable exponential decay rate for infections. Exploiting the monotone depletion of susceptible populations, we construct a robust terminal set and safe backup policy. This structure ensures recursive feasibility and finite-horizon closed-loop exponential decay, and it certifies the existence of a globally stabilizing feasible continuation under bounded worst-case transmission rates. Numerical simulations on a 14-county Massachusetts network under a variant-induced surge show that, with administrative rate limits, reactive myopic control fails whereas MPC anticipates the shock and maintains exponential decay with lower isolation burden.