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Modelling optimal lockdowns with waning immunity

Author

Listed:
  • Aditya Goenka

    (University of Birmingham [Birmingham])

  • Lin Liu

    (University of Liverpool)

  • Manh-Hung Nguyen

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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.

Suggested Citation

  • Aditya Goenka & Lin Liu & Manh-Hung Nguyen, 2024. "Modelling optimal lockdowns with waning immunity," Post-Print hal-04028181, HAL.
    • Handle: RePEc:hal:journl:hal-04028181
    DOI: 10.1007/s00199-022-01468-8
    as

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