  As a common strategy of contagious disease containment, lockdowns will
inevitably weaken the economy. The ongoing COVID-19 pandemic underscores the
trade-off arising from public health and economic cost. An optimal lockdown
policy to resolve this trade-off is highly desired. Here we propose a
mathematical framework of pandemic control through an optimal stabilizing
non-uniform lockdown, where our goal is to reduce the economic activity as
little as possible while decreasing the number of infected individuals at a
prescribed rate. This framework allows us to efficiently compute the optimal
stabilizing lockdown policy for general epidemic spread models, including both
the classical SIS/SIR/SEIR models and a new model of COVID-19 transmissions. We
demonstrate the power of this framework by analyzing publicly available data of
inter-county travel frequencies to analyze a model of COVID-19 spread in the 62
counties of New York State. We find that an optimal stabilizing lockdown based
on epidemic status in April 2020 would have reduced economic activity more
stringently outside of New York City compared to within it, even though the
epidemic was much more prevalent in New York City at that point. Such a
counterintuitive result highlights the intricacies of pandemic control and
sheds light on future lockdown policy design.
