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A parsimonious model of optimal social distancing and vaccination during an outbreak

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  • Gori, Luca
  • Manfredi, Piero
  • Marsiglio, Simone
  • Sodini, Mauro

Abstract

Motivated by the complicated control issues of COVID-19, this article aims at investigating the optimal control of an epidemic of a Susceptible-Infective-Removed-Susceptible (SIRS) infection, where social distancing is the only control action in a first stage, whereas a combination of social distancing and vaccination is available in a second stage. The resulting two-control optimal problem is set within a parsimonious economic framework in which a social planner minimises an objective function weighting epidemiological and economic costs by choosing the strength of social distancing in the first stage and both social distancing and the extent of an income tax to finance vaccination in the second stage. The article shows (i) how to mix social distancing and vaccination depending on the planner's degree of rationality; (ii) the importance of the planner's expectation about the date of vaccine arrival, and how the actual effi cacy of the vaccine against the infection can affect the optimal social distancing policy in the pre-vaccination period, and (iii) the use of the social distancing instrument as the only optimal control under vaccine rationing.

Suggested Citation

  • Gori, Luca & Manfredi, Piero & Marsiglio, Simone & Sodini, Mauro, 2023. "A parsimonious model of optimal social distancing and vaccination during an outbreak," GLO Discussion Paper Series 1263, Global Labor Organization (GLO).
    • Handle: RePEc:zbw:glodps:1263
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    References listed on IDEAS

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    1. Martin S Eichenbaum & Sergio Rebelo & Mathias Trabandt, 2021. "The Macroeconomics of Epidemics [Economic activity and the spread of viral diseases: Evidence from high frequency data]," The Review of Financial Studies, Society for Financial Studies, vol. 34(11), pages 5149-5187.
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    3. Luca GORI & Enrico LUPI & Piero MANFREDI & Mauro SODINI, 2020. "A Contribution to the Theory of Economic Development and the Demographic Transition: Fertility Reversal under the HIV Epidemic," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 86(2), pages 125-155, June.
    4. Marion Davin & Mouez Fodha & Thomas Seegmuller, 2023. "Environment, public debt, and epidemics," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 25(6), pages 1270-1303, December.
    5. Glover, Andrew & Heathcote, Jonathan & Krueger, Dirk, 2022. "Optimal age-Based vaccination and economic mitigation policies for the second phase of the covid-19 pandemic," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    6. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Epidemics and macroeconomic outcomes: Social distancing intensity and duration," Journal of Mathematical Economics, Elsevier, vol. 93(C).
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    Cited by:

    1. Buccella, Domenico & Fanti, Luciano & Gori, Luca, 2023. "The disclosure decision game: Subsidies and incentives for R&D activity," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 11-26.

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    More about this item

    Keywords

    Infectious diseases; COVID-19 transmission dynamics and interventions; Social distancing; Vaccination;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • J1 - Labor and Demographic Economics - - Demographic Economics
    • J22 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Time Allocation and Labor Supply
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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