Optimal policy during an epidemic includes depressing economic activity to slow down the outbreak. Sometimes, these decisions are left to local authorities (e.g. states). This creates an externality, as the outbreak does not respect states' boundaries. The externality directly exacerbates the outbreak. Indirectly, it creates a free-rider problem, because local policymakers pass the cost of fighting the outbreak on to other states. A standard system of distortionary taxes and lump-sum transfers can implement the optimal allocation, with higher tax rates required if states behave strategically. A strategic system of taxes and transfers, rewarding states which depress their economies more than average, improves the outcomes by creating a race-to-the-bottom type of response. In a symmetric equilibrium, the optimal tax rate is lower if states behave strategically.