Laura F. White

Mahtab Talaei, Alex Olshevsky, Laura F. White et al.

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.

Mahtab Talaei, Apostolos I. Rikos, Alex Olshevsky et al.

Motivated by the swift global transmission of infectious diseases, we present a comprehensive framework for network-based epidemic control. Our aim is to curb epidemics using two different approaches. In the first approach, we introduce an optimization strategy that optimally reduces travel rates. We analyze the convergence of this strategy and show that it hinges on the network structure to minimize infection spread. In the second approach, we expand the classic SIR model by incorporating and optimizing quarantined states to strategically contain the epidemic. We show that this problem reduces to the problem of matrix balancing. We establish a link between optimization constraints and the epidemic's reproduction number, highlighting the relationship between network structure and disease dynamics. We demonstrate that applying augmented primal-dual gradient dynamics to the optimal quarantine problem ensures exponential convergence to the KKT point. We conclude by validating our approaches using simulation studies that leverage public data from counties in the state of Massachusetts.