Optimal Control of Pandemic Dynamics via Model Predictive Control : A Health-Economic Trade-off Analysis

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Melhani, Lokman Rachid ; Grüne, Lars ; Sferlazza, Antonino ; Adorno, Dominique Persano ; D'Ippolito, Filippo ; Firenze, Alberto:
Optimal Control of Pandemic Dynamics via Model Predictive Control : A Health-Economic Trade-off Analysis.
Bayreuth ; Palermo , 2026 . - 17 S.
DOI: https://doi.org/10.48550/arXiv.2607.11306

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Abstract

This paper addresses the optimal control of epidemic dynamics under conflicting socio-economic objectives. We propose an economic Model Predictive Control (MPC) framework, applied to an extended SEIR-V (Susceptible-Exposed-Infected-Recovered-Vaccinated) compartmental model to govern the spread of an infectious disease while minimizing economic disruption. The control problem is formulated as a constrained nonlinear optimization problem, in which the controller dynamically adjusts social interaction levels (transmission rate beta) and vaccination efforts to minimize a composite cost function that penalizes fatalities, healthcare capacity violations, and economic losses. We conduct a rigorous sensitivity analysis of the prediction horizon N, demonstrating that the closed loop is robust to the horizon choice and that N = 35 days minimizes the realized cost. Furthermore, both the closed-loop solution and an open-loop turnpike analysis across diverse initial conditions reveal that the celebrated "Hammer and Dance" mitigation strategy emerges naturally as the mathematical optimum: the optimal trajectories anchor to a unique suppression turnpike (maximum lockdown) to drive hospitalizations toward the disease-free equilibrium before progressively reopening the economy. Through a turnpike-based argument we establish practical asymptotic stability of the optimal operating point, providing a mathematically grounded decision-support tool for pandemic policy.