Optimal Prevention and Elimination of Infectious Diseases

This article studies the optimal intertemporal allocation of resources devoted to the prevention of deterministic infectious diseases that admit an endemic steady- state. Under general assumptions, the optimal control problem is shown to be formally similar to an optimal growth model with endogenous discounting. The optimal dynamics then depends on the interplay between the epidemiological characteristics of the disease, the labour productivity and the degree of inter- generational equity. Phase diagrams analysis reveal that multiple trajectories, which converge to endemic steady-states with or without prevention or to the elimination of the disease, are feasible. Elimination implies initially a larger prevention than in other trajectories, but after a .nite date, prevention is equal to zero. This .sooner-the-better. strategy is shown to be optimal if the pure discount rate is su¢ ciently low.