  Initial hopes of quickly eradicating the COVID-19 pandemic proved futile, and
the goal shifted to controlling the peak of the infection, so as to minimize
the load on healthcare systems. To that end, public health authorities
intervened aggressively to institute social distancing, lock-down policies, and
other Non-Pharmaceutical Interventions (NPIs). Given the high social,
educational, psychological, and economic costs of NPIs, authorities tune them,
alternatively tightening up or relaxing rules, with the result that, in effect,
a relatively flat infection rate results. For example, during the summer in
parts of the United States, daily infection numbers dropped to a plateau. This
paper approaches NPI tuning as a control-theoretic problem, starting from a
simple dynamic model for social distancing based on the classical SIR epidemics
model. Using a singular-perturbation approach, the plateau becomes a
Quasi-Steady-State (QSS) of a reduced two-dimensional SIR model regulated by
adaptive dynamic feedback. It is shown that the QSS can be assigned and it is
globally asymptotically stable. Interestingly, the dynamic model for social
distancing can be interpreted as a nonlinear integral controller. Problems of
data fitting and parameter identifiability are also studied for this model. The
paper also discusses how this simple model allows for meaningful study of the
effect of population size, vaccinations, and the emergence of second waves.
