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Modelling optimal lockdowns with waning immunity

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  • Published: 29 November 2022
  • Volume 77, pages 197–234, (2024)
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Modelling optimal lockdowns with waning immunity
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  • Aditya Goenka  ORCID: orcid.org/0000-0002-7726-11831,
  • Lin Liu2 &
  • Manh-Hung Nguyen3 
  • 834 Accesses

  • 13 Citations

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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.

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Authors and Affiliations

  1. Department of Economics, University of Birmingham, Birmingham, England

    Aditya Goenka

  2. Management School, University of Liverpool, Liverpool, England

    Lin Liu

  3. Toulouse School of Economics, INRAE, University of Toulouse Capitole, Toulouse, France

    Manh-Hung Nguyen

Authors
  1. Aditya Goenka
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  2. Lin Liu
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  3. Manh-Hung Nguyen
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Correspondence to Aditya Goenka.

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We thank seminar participants in Birmingham, Kansas, Macau, NYUAD, and the T2M Conference 2022, the anonymous referee, and the Associate Editor for their helpful comments. The usual disclaimer applies. Manh-Hung Nguyen acknowledges support from ANR under grant ANR-17-EURE-0010 (Investissements d’Avenir program).

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Goenka, A., Liu, L. & Nguyen, MH. Modelling optimal lockdowns with waning immunity. Econ Theory 77, 197–234 (2024). https://doi.org/10.1007/s00199-022-01468-8

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  • Received: 28 August 2020

  • Accepted: 10 October 2022

  • Published: 29 November 2022

  • Issue Date: February 2024

  • DOI: https://doi.org/10.1007/s00199-022-01468-8

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Keywords

  • Covid-19
  • SIRS model
  • Mortality
  • Lockdown
  • Quarantine
  • Sufficiency conditions
  • Self-isolation
  • Infectious diseases
  • NPI
  • Endogenous discounting

JEL Classification

  • E13
  • E22
  • D15
  • D50
  • D63
  • I10
  • I15
  • I18
  • O41
  • C61
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Mathematical Economic Epidemiology Models

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