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Optimal Control of Prevention and Treatment in a Basic Macroeconomic-Epidemiological Model

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Document pages: 17 pages

Abstract: We analyze the optimal control of disease prevention and treatment in a basicSIS model. We develop a simple macroeconomic setup in which the social plannerdetermines how to optimally intervene, through income taxation, in order tominimize the social cost, inclusive of infection and economic costs, of thespread of an epidemic disease. The disease lowers economic production and thusincome by reducing the size of the labor force employed in productiveactivities, tightening thus the economy s overall resources constraint. Weconsider a framework in which the planner uses the collected tax revenue tointervene in either prevention (aimed at reducing the rate of infection) ortreatment (aimed at increasing the speed of recovery). Both optimal preventionand treatment policies allow the economy to achieve a disease-free equilibriumin the long run but their associated costs are substantially different alongthe transitional dynamic path. By quantifying the social costs associated withprevention and treatment we determine which policy is most cost-effective underdifferent circumstances, showing that prevention (treatment) is desirablewhenever the infectivity rate is low (high).

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