Network Epidemic Control via Model Predictive Control
This work provides a safety-critical MPC framework for epidemic control that guarantees recursive feasibility and exponential decay, addressing the need for adaptive policies that balance suppression and societal costs.
The authors formulate an infinite-horizon optimal control problem for a networked epidemic model and derive a Model Predictive Control (MPC) framework that enforces exponential decay of infections via a spectral constraint. Simulations on a 14-county Massachusetts network show that MPC maintains exponential decay with lower isolation burden compared to myopic control during a variant-induced surge.
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.