Abstract
Although modeling studies are focused on the control of SIR-based systems describing epidemic data sets (particularly the COVID-19), few of them present a formal dynamic characterization in terms of equilibrium sets and stability. Such concepts can be crucial to understand not only how the virus spreads in a population, but also how to tailor government interventions such as social distancing, isolation measures, etc. The objective of this work is to provide a full dynamic characterization of SIR-type systems under single-interval control actions and, based on it, to find the control action that produces the smallest number of infected individuals at the end of the epidemic that avoids second wave outbreaks. Simulations illustrate the benefits of the aforementioned results in terms of the herd immunity threshold.