Multitask learning and nonlinear optimal control of the COVID-19 outbreak: A geometric programming approach

In this paper we propose a data-driven model for the spread of SARS-CoV-2 and use it to design optimal control strategies of human-mobility restrictions that both curb the epidemic and minimize the economic costs associated with implementing non-pharmaceutical interventions. We develop an extension of the SEIR epidemic model that captures the effects of changes in human mobility on the spread of the disease. The parameters of our data-driven model are learned using a multitask learning approach that leverages both data on the number of deaths across a set of regions, and cellphone data on individuals' mobility patterns specific to each region. We propose an optimal control problem on this data-driven model with a tractable solution provided by geometric programming. The result of this framework is a mobility-based intervention strategy that curbs the spread of the epidemic while obeying a budget on the economic cost incurred. Furthermore, in the absence of a straightforward mapping from human mobility data to economic costs, we propose a practical method by which a budget on economic losses incurred may be chosen to eliminate excess deaths due to over-utilization of hospital resources. Our results are demonstrated with numerical simulations using real data from the Philadelphia metropolitan area.