  Several non-pharmaceutical interventions have been proposed to control the
spread of the COVID-19 pandemic. On the large scale, these empirical solutions,
often associated with extended and complete lockdowns, attempt to minimize the
costs associated with mortality, economic losses and social factors, while
being subject to constraints such as finite hospital capacity. Here we pose the
question of how to mitigate pandemic costs subject to constraints by adopting
the language of optimal control theory. This allows us to determine top-down
policies for the nature and dynamics of social contact rates given an
age-structured model for the dynamics of the disease. Depending on the relative
weights allocated to life and socioeconomic losses, we see that the optimal
strategies range from long-term social-distancing only for the most vulnerable,
to partial lockdown to ensure not over-running hospitals, to alternating-shifts
with significant reduction in life and/or socioeconomic losses. Crucially,
commonly used strategies that involve long periods of broad lockdown are almost
never optimal, as they are highly unstable to reopening and entail high
socioeconomic costs. Using parameter estimates from data available for Germany
and the USA, we quantify these policies and use sensitivity analysis in the
relevant model parameters and initial conditions to determine the range of
robustness of our policies. Finally we also discuss how bottom-up behavioral
changes can also change the dynamics of the pandemic and show how this in
tandem with top-down control policies can mitigate pandemic costs even more
effectively.
