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Modeling optimal quarantines with waning immunity

Author

Listed:
  • Aditya Goenka

    (University of Birmingham)

  • Lin Liu

    (University of Liverpool)

  • Manh-Hung Nguyen

    (Toulouse School of Economics)

Abstract
This paper studies continuing optimal quarantines (can also be interpreted as lockdowns or self-isolation) in the long run if a disease (Covid-19) is endemic and immunity can fail, i.e. the disease has SIRS dynamics. We model how the disease related mortality affects optimal choices in a dynamic general equilibrium neoclassical growth framework. An extended welfare function that incorporates loss from mortality is used. Without welfare loss from mortality, in the long run even if there is continuing mortality, it is not optimal to impose a quarantine. We characterize the optimal decision of quarantines and how the disease endemic steady state changes with effectiveness of quarantine, productivity of working from home, rate of mortality from the disease, and failure of immunity. We also give the sufficiency conditions for economic models with SIRS dynamics - 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, 2021. "Modeling optimal quarantines with waning immunity," Discussion Papers 21-10, Department of Economics, University of Birmingham.
    • Handle: RePEc:bir:birmec:21-10
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    Cited by:

    1. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2021. "COVID-19 and a Green Recovery?," Economic Modelling, Elsevier, vol. 104(C).

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    More about this item

    Keywords

    Infectious diseases; Covid-19; SIRS model; mortality; quarantine; sufficiency conditions; lockdown; self-isolation;
    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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