Data-driven optimal control of a SEIR model for COVID-19

Liu, Hailiang; Tian, Xuping

Since the first case of COVID-19 in December 2019, a total of $11,357,322$ confirmed cases in the US and $55,624,562$ confirmed cases worldwide have been reported, up to November 17, 2020, evoking fear locally and internationally. In particular, the coronavirus is surging nationwide at this time. In this paper, we investigate a basic Susceptible-Exposed-Infectious-Recovered (SEIR) model and calibrate the model parameters to the reported data. We also attempt to forecast the evolution of the outbreak over a relatively short time period and provide scheduled optimal controls of the COVID-19 epidemic. We provide efficient numerical algorithms based on a generalized Pontryagin Maximum Principle associated with the optimal control theory. Numerical experiments demonstrate the effective performance of the proposed model and its numerical approximations.