Minimizing the financial cost of COVID-19 using optimal control

The COVID-19 pandemic has already caused hundreds of thousands of deaths worldwide. Countries have implemented national lockdowns in an effort to curtail the loss of human life. Consequently, they have had major economic repercussions due to joblessness and other factors. In an attempt to decrease economic impact, Sweden chose to implement a relatively lax lockdown strategy. However, when compared to other neighboring countries Sweden ended up with more COVID-19 cases and little economic benefit. We are interested in investigating COVID-19 control strategies that minimize financial cost. To this end, we formulate a deterministic ordinary differential equation model for the spread of COVID-19 with a control term limiting disease spread. In order to describe the cost of the pandemic, we use a payoff functional consisting of two parts. First, we have the cost of labor loss, which increases as the control increases. Second, we have the cost of hospitalization, which does not depend directly on the control. We use optimal control and numerical simulations to find control schemes that minimize the financial costs of COVID-19 that arise from loss of labor and hospitalization.