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A simple planning problem for COVID-19 lockdown: a dynamic programming approach

Author

Listed:
  • Alessandro Calvia

    (LUISS University)

  • Fausto Gozzi

    (LUISS University)

  • Francesco Lippi

    (LUISS University
    Einaudi Institute for Economics and Finance)

  • Giovanni Zanco

    (Università di Siena)

Abstract

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton–Jacobi–Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.

Suggested Citation

  • Alessandro Calvia & Fausto Gozzi & Francesco Lippi & Giovanni Zanco, 2024. "A simple planning problem for COVID-19 lockdown: a dynamic programming approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 169-196, February.
    • Handle: RePEc:spr:joecth:v:77:y:2024:i:1:d:10.1007_s00199-023-01493-1
    DOI: 10.1007/s00199-023-01493-1
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    References listed on IDEAS

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    Cited by:

    1. Raouf Boucekkine & Ted Loch-Temzelides, 2024. "Introduction to the special issue on mathematical economic epidemiology models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 1-7, February.
    2. Alessandro Ramponi & Maria Elisabetta Tessitore, 2024. "Optimal Social and Vaccination Control in the SVIR Epidemic Model," Mathematics, MDPI, vol. 12(7), pages 1-17, March.

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    More about this item

    Keywords

    Controlled SIRD model; Optimal lockdown policies; Optimal control with state space constraints; Optimality conditions; Viscosity solutions;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production
    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • I15 - Health, Education, and Welfare - - Health - - - Health and Economic Development
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health

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