Optimal control of COVID-19 infection rate with social costs.

The COVID-19 pandemic has posed a policy making crisis where efforts to slow down or end the pandemic conflict with economic priorities. This paper provides mathematical analysis of optimal disease control policies with idealized compartmental models for disease propagation and simplistic models of social and economic costs. The optimal control strategies are categorized as 'suppression' and 'mitigation' strategies and are analyzed in both deterministic and stochastic models. In the stochastic model, vaccination at an uncertain time is taken into account.