Document de travail

Modeling optimal quarantines under infectious disease related mortality

Aditya Goenka, Lin Liu et Manh-Hung Nguyen


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.


Infectious diseases; Covid-19; SIS model; mortality; sufficiency conditions; economic growth; lockdown; quarantine; self-isolation.;


Aditya Goenka, Lin Liu et Manh-Hung Nguyen, « Modeling optimal quarantines under infectious disease related mortality », TSE Working Paper, n° 20-1136, août 2020.

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Publié dans

TSE Working Paper, n° 20-1136, août 2020