Optimal Lockdown for Pandemic Stabilization

Ma, Qianqian; Liu, Yang-Yu; Olshevsky, Alex

We consider the problem of pandemic stabilization through a non-uniform lockdown, where our goal is to reduce economic activity as little as possible while sending the number of infected patients to zero at a prescribed rate. We consider several different models of epidemic spread over networks, including SIS/SIR/SEIR models as well as a new model of COVID-19 transmissions with symptomatic and asymptomatic individuals. We provide two efficient algorithms which can efficiently compute the optimal lockdown, with one of our algorithms having a running time which explicitly scales only linearly in the number of edges in the network and is applicable to the vast majority of epidemic models we have tested. Our second algorithm has an explicit scaling which is cubic in the number of nodes in the network, but is applicable without any assumptions. We further demonstrate a number of previously-unknown counter-intuitive phenomena by numerically computing the optimal lockdown on a number of test cases. For example, we show that in a variety of random graph models, node centrality and population have little effect on the value of a lockdown at a node unless they take on extreme values. Most surprisingly, we use publicly available data on inter-county travel frequencies to analyze a model of COVID-19 spread in the 62 counties of New York State; we compute that an optimal stabilizing shutdown based on the state of the epidemic in April 2020 would have reduced 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.