Cost Optimization in the SIS Model of Infectious Disease with Treatment

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Abstract
We consider the intertemporal social optimization problem of minimizing the present value of the costs incurred from both disease and treatment. Though the analysis is complicated by the analytical failure of concavity, we are able to substantially characterize both the long run equilibria and the adjustment paths. The cost minimizing program is shown to exhibit decreased levels of treatment at higher disease levels. The socially optimal program is compared to individually rational behavior and the inefficiencies in private behavior from the infection externality are shown to cause increases in the equilibrium rate of infection.

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