Minimizing the epidemic final size while containing the infected peak prevalence in SIR systems

SERENO, JUAN; ANDERSON, ALEJANDRO; FERRAMOSCA, ANTONIO; HERNANDEZ VARGAS, ESTEBAN ABELARDO; GONZÁLEZ, ALEJANDRO HERNÁN

AUTOMATICA

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2022

0005-1098

Mathematical models are critical to understand the spread of pathogens in a population and evaluate the effectiveness of non-pharmaceuticalinterventions (NPIs). A plethora of optimal strategies have been recently developed to minimize either the infected peak prevalence (IPP)or the epidemic final size (EFS). While most of them optimize a simple cost function along a fixed finite-time horizon, no consensushas been reached about how to simultaneously handle the IPP and the EFS, while minimizing the intervention?s side effects. In thiswork, based on a new characterization of the dynamical behavior of SIR-type models under control actions (including the stability ofequilibrium sets in terms of the herd immunity), we study how to minimize the EFS while keeping the IPP controlled at any time. Aprocedure is proposed to tailor NPIs by separating transient from stationary control objectives: the potential benefits of the strategy areillustrated by a detailed analysis and simulation results related to the COVID-19 pandemic.