  Social distancing strategies have been adopted by governments to manage the
COVID-19 pandemic, since the first outbreak began. However, further epidemic
waves keep out the return of economic and social activities to their standard
levels of intensity. Social distancing interventions based on control theory
are needed to consider a formal dynamic characterization of the implemented
SIR-type model to avoid unrealistic objectives and prevent further outbreaks.
The objective of this work is twofold: to fully understand some dynamical
aspects of SIR-type models under control actions (associated with second waves)
and, based on it, to propose a switching non-linear model predictive control
that optimize the non-pharmaceutical measures strategy. Opposite to other
strategies, the objective here is not just to minimize the number of infected
individuals at any time, but to minimize the final size of the epidemic while
minimizing the time of social restrictions and avoiding the infected prevalence
peak to overpass a maximum established by the healthcare system capacity.
Simulations illustrate the benefits of the aforementioned proposal.
