The COVID-19 pandemic has killed millions across the globe and government responses have led to tens of millions of jobs lost. This paper combines the SIR epidemic model with a frictional labor market to examine the interaction between infection, wages and unemployment. The labor market is not efficient during the pandemic. Optimal policies show that it is often optimal to shut down businesses and impose a quarantine before the pandemic peaks. A quarantine itself is not enough, however, and must be complemented by additional policies. The policies are not unique and include a Pigouvian "infection tax" on those infected, a tax on susceptible individuals, higher unemployment benefits and a tax on vacancy creation. All policies are state dependent and depend both on the number of unemployed and on the number of infected.
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