The Optimal Control of Infectious Diseases via Prevention and Treatment

Abstract

This paper fully characterizes the optimal control of a recur- rent infectious disease through the use of prevention and treatment. We find that under centralized decision making, treatment induces positive destabilizing feed- back effects, while prevention induces negative stabilizing feedback effects. Under decentralized decision making, these effects create elements of strategic comple- mentarities and substitutabilities, respectively. While optimal treatment pushes prevalence towards the extremes, optimal prevention pushes it towards interior so- lutions. As a result, the dynamic system may admit multiple steady states and the optimal policy may be path dependent. We find that steady state prevalence levels in decentralized equilibrium must be equal to or higher than the socially optimal levels. While steady state treatment levels under decentralization are typically so- cially optimal, steady state prevention (if used) is socially suboptimal. Last, we derive a Pigouvian subsidy scheme that decentralizes the socially optimal outcome.