IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v77y2024i1d10.1007_s00199-023-01493-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-023-01493-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-023-01493-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:77:y:2024:i:1:d:10.1007_s00199-023-01493-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.