Optimal control in pandemics

During a pandemic, there are conflicting demands that arise from public health and socioeconomic costs. Lockdowns are a common way of containing infections, but they adversely affect the economy. We study the question of how to minimize the socioeconomic damage of a lockdown while still containing infections. Our analysis is based on the SIR model, which we analyze using a clock set by the virus. This use of the "virus time" permits a clean mathematical formulation of our problem. We optimize the socioeconomic cost for a fixed health cost and arrive at a strategy for navigating the pandemic. This involves adjusting the level of lockdowns in a controlled manner so as to minimize the socioeconomic cost.