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Modelling optimal lockdowns with waning immunity

Author

Listed:
  • Aditya Goenka

    (University of Birmingham)

  • Lin Liu

    (University of Liverpool)

  • Manh-Hung Nguyen

    (University of Toulouse Capitole)

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," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 197-234, February.
    • Handle: RePEc:spr:joecth:v:77:y:2024:i:1:d:10.1007_s00199-022-01468-8
    DOI: 10.1007/s00199-022-01468-8
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    More about this item

    Keywords

    Covid-19; SIRS model; Mortality; Lockdown; Quarantine; Sufficiency conditions; Self-isolation; Infectious diseases; NPI; Endogenous discounting;
    All these keywords.

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I10 - Health, Education, and Welfare - - Health - - - General
    • I15 - Health, Education, and Welfare - - Health - - - Health and Economic Development
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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