Optimal Fixed Lockdown for Pandemic Control

As a common strategy of contagious disease containment, lockdowns inevitably have economic cost. The ongoing COVID-19 pandemic underscores the tradeoff arising from public health and economic cost. An optimal lockdown policy to resolve this tradeoff is desired. Here, we propose a mathematical framework of pandemic control through an optimal fixed stabilizing nonuniform 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 susceptible-infectious-susceptible (SIS)/susceptible-infectious-recovered/susceptible-exposed-infectious-recovered models and a model of COVID-19 transmissions. We demonstrate the power of this framework by analyzing publicly available data of intercounty 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. This finding holds for a variety of epidemic models and parameters from the literature, and is robust to errors in travel rates, different cost functions, and potential urban–rural transmission spread differentials.