Optimal single-interval control for SIR-type systems

GONZÁLEZ, ALEJANDRO HERNÁN; FERRAMOSCA, ANTONIO; HERNANDEZ VARGAS, ESTEBAN ABELARDO

Paris

Workshop; 8th IFAC Workshop on Control Application of Optimization (CAO2022); 2022

IFAC

Although modeling studies are focused on the control of SIR-based systemsdescribing epidemic data sets (recently coming from the dierent variants of the SARS-CoV-2), few of them present a formal dynamic characterization in terms of the two mainindexes: the infected peak prevalence (IPP), and the nal epidemic size (EFS). Theseindices are directly related to equilibrium sets and stability, which are crucial concepts tounderstand what the government can (and cannot) do to handle an epidemic, by means ofnon-pharmaceutical interventions such as social distancing, isolation measures, mask-wearing,among others. The objective of this work is to provide a theoretical single interval controlstrategy that simultaneously minimizes the EFS while maintaining the IPP arbitrary low,according to health system capacity limitations. Several simulations illustrate the true role ofthe herd immunity threshold and provide new insight into the way authorities may act.