Modelling optimal lockdowns with waning immunity

Aditya Goenka, Lin Liu () and Manh-Hung Nguyen ()
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Lin Liu: University of Liverpool
Manh-Hung Nguyen: University of Toulouse Capitole

Economic Theory, 2024, vol. 77, issue 1, No 7, 197-234

Abstract: Abstract This paper studies continuing optimal lockdowns (can also be interpreted as quarantines or self-isolation) in the long run if a disease (Covid-19) is endemic and immunity can fail, that is, the disease has SIRS dynamics. We model how disease related mortality affects the optimal choices in a dynamic general equilibrium neoclassical growth framework. An extended welfare function that incorporates loss from mortality is used. In a disease endemic steady state, without this welfare loss even if there is continuing mortality, it is not optimal to impose even a partial lockdown. We characterize how the optimal restriction and equilibrium outcomes vary with the effectiveness of the lockdown, the productivity of working from home, the rate of mortality from the disease, and failure of immunity. We provide the sufficiency conditions for economic models with SIRS dynamics with disease related mortality–a class of models which are non-convex and have endogenous discounting so that no existing results are applicable.

Keywords: Covid-19; SIRS model; Mortality; Lockdown; Quarantine; Sufficiency conditions; Self-isolation; Infectious diseases; NPI; Endogenous discounting (search for similar items in EconPapers)
JEL-codes: C61 D15 D50 D63 E13 E22 I10 I15 I18 O41 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00199-022-01468-8

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