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Optimal Control of an Epidemic with Intervention Design
arXiv:2503.22928v2 Announce Type: replace-cross
Abstract: This paper investigates the optimal control of an epidemic governed by a SEIR model with operational delays in vaccination and non pharmaceutical interventions. We address the mathematical challenge of imposing hard healthcare capacity constraints (e.g., ICU limits) over an infinite time horizon. To rigorously bridge the gap between theoretical constraints and numerical tractability, we employ a variational framework based on Moreau--Yosida regularization and establish the connection between finite- and infinite-horizon solutions via $\Gamma$-convergence. The necessary conditions for optimality are derived using the Pontryagin Maximum Principle, allowing for the characterization of singular regimes where the optimal strategy maintains the infection level precisely at the capacity boundary. Numerical simulations illustrate these theoretical findings, quantifying the shadow prices of infection and costs associated with intervention delays.
Abstract: This paper investigates the optimal control of an epidemic governed by a SEIR model with operational delays in vaccination and non pharmaceutical interventions. We address the mathematical challenge of imposing hard healthcare capacity constraints (e.g., ICU limits) over an infinite time horizon. To rigorously bridge the gap between theoretical constraints and numerical tractability, we employ a variational framework based on Moreau--Yosida regularization and establish the connection between finite- and infinite-horizon solutions via $\Gamma$-convergence. The necessary conditions for optimality are derived using the Pontryagin Maximum Principle, allowing for the characterization of singular regimes where the optimal strategy maintains the infection level precisely at the capacity boundary. Numerical simulations illustrate these theoretical findings, quantifying the shadow prices of infection and costs associated with intervention delays.
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