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 labor productivity and the degree of intergenerational equity. Phase diagrams analysis reveals 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 finite date, prevention is equal to zero. This “sooner-the-better” strategy is shown to be optimal if the pure discount rate is sufficiently low.

本文研究了用于预防流行性稳态的确定性传染病的资源的最佳跨期分配。在一般假设下，最优控制问题在形式上类似于具有内生贴现的最优增长模型。然后，最佳动态取决于该疾病的流行病学特征，劳动生产率和代际平等程度之间的相互作用。相图分析表明，在有或没有预防或消除疾病的情况下，收敛到地方性稳态的多种轨迹是可行的。消除起初意味着比其他轨迹更大的预防，但是在有限日期之后，预防等于零。