COVID-19 and Unemployment: A Novel Bi-Level Optimal Control Model

Since COVID-19 was declared as a pandemic in March 2020, the world's major preoccupation has been to curb it while preserving the economy and reducing unemployment. This paper uses a novel Bi-Level Dynamic Optimal Control model (BLDOC) to coordinate control between COVID-19 and unemployment. The COVID-19 model is the upper level while the unemployment model is the lower level of the bi-level dynamic optimal control model. The BLDOC model's main objectives are to minimize the number of individuals infected with COVID-19 and to minimize the unemployed individuals, and at the same time minimizing the cost of the containment strategies. We use the modified approximation Karush-Kuhn- Tucker (KKT) conditions with the Hamiltonian function to handle the bi-level dynamic optimal control model. We consider three control variables: The first control variable relates to government measures to curb the COVID-19 pandemic, i.e., quarantine, social distancing, and personal protection; and the other two control variables relate to government interventions to reduce the unemployment rate, i.e., employment, making individuals qualified, creating new jobs reviving the economy, reducing taxes. We investigate four different cases to verify the effect of control variables. Our results indicate that rather than focusing exclusively on only one problem, we need a balanced trade-off between controlling each.