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Mathematical models are instrumental to forecast the spread of pathogens andto evaluate the effectiveness of non-pharmaceutical measures. A plethora ofoptimal strategies has been recently developed to minimize either the infectedpeak prevalence (IPP) or the epidemic final size (EFS). While most of thecontrol strategies optimize a simple cost function along a fixed finite-timehorizon, no consensus has been reached about how to simultaneously handle theIPP, the EFS, and the avoiding of new cycles of infections rebounding. In thiswork, based on the characterization of the dynamical behaviour of SIR-typemodels under control actions (including the stability of equilibrium sets, interms of the herd immunity), it is studied how to minimize the EFS whilekeeping - at any time - the IPP controlled. A procedure is proposed to tailornon-pharmaceutical interventions by separating transient from stationarycontrol objectives and the potential benefits of the strategy are illustratedby a detailed analysis and simulation results related to the COVID-19 pandemic.

Minimizing the Epidemic Final Size while Containing the Infected Peak Prevalence in SIR Systems