Optimal single-interval control for SIR-type systems

Although modeling studies are focused on the control of SIR-based systems describing epidemic data sets, few them present a formal dynamic characterization in terms two main indexes: infected peak prevalence (IPP) and final size (EFS). These indices directly related to equilibrium sets stability, which crucial concepts understand what kind non-pharmaceutical interventions (social distancing, isolation measures, mask-wearing, etc.) can be implemented handle an epidemic. The objective this work is provide theoretical single-interval strategy that simultaneously minimizes EFS while maintaining IPP arbitrary low, according health system capacity limitations. Several simulations illustrate true role herd immunity threshold new insight into way authorities may act.