An optimal control framework for mitigating cross-border epidemic spread through testing of incoming travelers and shows the optimal control is bang bang by excluding singular arcs via Hamiltonian analysis and derive the optimal switching time.
Abstract
We propose an optimal control framework for mitigating cross-border epidemic spread through testing of incoming travelers. The general model considers multiple countries with SEIR dynamics, while the explicit analysis focuses on a simplified two country SIR system without vaccination. The control variable is a time measurable function representing the testing rate. For the two country SIR case, we show the optimal control is bang bang by excluding singular arcs via Hamiltonian analysis and derive the optimal switching time. Our results offer theoretical insights and practical guidelines for designing cost effective border testing policies. We then present numerical simulations for the optimal control in the two population setting.
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