Goenka, Aditya, Liu, Lin and Nguyen, Manh-Hung (2020) Modeling optimal quarantines under infectious disease related mortality. TSE Working Paper, n. 20-1136, Toulouse

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Abstract

This paper studies optimal quarantines (can also be interpreted as lockdowns or selfisolation)
when there is an infectious disease with SIS dynamics and infections can
cause disease related mortality in a dynamic general equilibrium neoclassical growth
framework. We characterize the optimal decision and the steady states and how these
change with changes in effectiveness of quarantine, productivity of working from home,
contact rate of disease and rate of mortality from the disease. A standard utilitarian
welfare function gives the counter-intuitive result that increasing mortality reduces
quarantines but increases mortality and welfare while economic outcomes and infections
are largely unaffected. With an extended welfare function incorporating welfare
loss due to disease related mortality (or infections generally) however, quarantines increase,
and the decreasing infections reduce mortality and increase economic outcomes.
Thus, there is no optimal trade-off between health and economic outcomes. We also
study sufficiency conditions and provide the first results in economic models with SIS
dynamics with disease related mortality - a class of models which are non-convex and
have endogenous discounting so that no existing results are applicable.