IDEAS home Printed from https://ideas.repec.org/p/hal/psewpa/hal-03693086.html
   My bibliography  Save this paper

A Time-Space Integro-Differential Economic Model of Epidemic Control

Author

Listed:
  • Carmen Camacho

    (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Rodolphe Desbordes

    (SKEMA Business School)

  • Davide Torre

    (SKEMA Business School - SKEMA Business School)

Abstract

In this paper we propose a time-space economic model to control the evolution and the spread of a disease. The underlying epidemiological model is formulated as a reaction-diffusion integro-differential partial differential equation. This specific model formulation, supported by empirical data, contains three different terms: a pure diffusion term, a linear growth term, and an integral term. These three terms capture different diffusion channels of a transmissible disease: a pure spatial diffusion effect, a local effect and a global effect. The decision maker aims at deciding the optimal effort to be implemented in order to control the number of infections and, at the same time, minimize the cost of treatment. We analyze both the finite and the infinite horizon cases, and provide the closed-form expression of the optimal policy to be implemented to control the epidemic while sustaining economic growth.

Suggested Citation

  • Carmen Camacho & Rodolphe Desbordes & Davide Torre, 2022. "A Time-Space Integro-Differential Economic Model of Epidemic Control," PSE Working Papers hal-03693086, HAL.
    • Handle: RePEc:hal:psewpa:hal-03693086
    Note: View the original document on HAL open archive server: https://hal.science/hal-03693086
    as

    Download full text from publisher

    File URL: https://hal.science/hal-03693086/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Boucekkine, R. & Camacho, C. & Fabbri, G., 2013. "Spatial dynamics and convergence: The spatial AK model," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2719-2736.
    2. Desbordes, Rodolphe, 2021. "Spatial dynamics of major infectious diseases outbreaks: A global empirical assessment," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    3. Bosi, Stefano & Camacho, Carmen & Desmarchelier, David, 2021. "Optimal lockdown in altruistic economies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    4. Cindy Cheng & Joan Barceló & Allison Spencer Hartnett & Robert Kubinec & Luca Messerschmidt, 2020. "COVID-19 Government Response Event Dataset (CoronaNet v.1.0)," Nature Human Behaviour, Nature, vol. 4(7), pages 756-768, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boucekkine, Raouf & Chakraborty, Shankha & Goenka, Aditya & Liu, Lin, 2024. "Economic epidemiological modelling: A progress report," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    2. Raouf Boucekkine & Shankha Chakraborty & Aditya Goenka & Lin Liu, 2024. "A Brief Tour of Economic Epidemiology Modelling," LIDAM Discussion Papers IRES 2024002, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    3. Francesco Bartaloni, 2021. "Existence of the Optimum in Shallow Lake Type Models with Hysteresis Effect," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 358-392, August.
    4. Carmen Camacho & Agustín Pérez-Barahona, 2017. "The diffusion of economic activity across space: a new approach," Working Papers halshs-01670532, HAL.
    5. Emmanuelle Augeraud-Véron & Raouf Boucekkine & Vladimir Veliov, 2019. "Distributed Optimal Control Models in Environmental Economics: A Review," AMSE Working Papers 1902, Aix-Marseille School of Economics, France.
    6. Paulo B. Brito, 2022. "The dynamics of growth and distribution in a spatially heterogeneous world," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 21(3), pages 311-350, September.
    7. Lalinsky, Tibor & Pál, Rozália, 2022. "Distribution of COVID-19 government support and its consequences for firm liquidity and solvency," Structural Change and Economic Dynamics, Elsevier, vol. 61(C), pages 305-335.
    8. Cui Zhang & Dandan Zhang, 2023. "Spatial Interactions and the Spread of COVID-19: A Network Perspective," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 383-405, June.
    9. David Desmarchelier & Thomas Lanzi, 2023. "Opinion Dynamics and Political Persuasion," Post-Print hal-04711036, HAL.
    10. Brock, William A. & Xepapadeas, Anastasios & Yannacopoulos, Athanasios N., 2014. "Optimal agglomerations in dynamic economics," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 1-15.
    11. W. A. Brock & A. Xepapadeas, 2015. "Modeling Coupled Climate, Ecosystems, and Economic Systems," Working Papers 2015.66, Fondazione Eni Enrico Mattei.
    12. Abel Brodeur & David Gray & Anik Islam & Suraiya Bhuiyan, 2021. "A literature review of the economics of COVID‐19," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1007-1044, September.
    13. Hayato Kato & Toshihiro Okubo, 2022. "The Resilience of FDI to Natural Disasters Through Industrial Linkages," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 82(1), pages 177-225, May.
    14. Ballestra, Luca Vincenzo, 2016. "The spatial AK model and the Pontryagin maximum principle," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 87-94.
    15. Keiichi Morimoto & Shiba Suzuki, 2022. "Ambiguity in a pandemic recession, asset prices, and lockdown policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1039-1070, October.
    16. Giorgio Fabbri & Fausto Gozzi & Andrzej Swiech, 2017. "Stochastic Optimal Control in Infinite Dimensions - Dynamic Programming and HJB Equations," Post-Print hal-01505767, HAL.
    17. Boucekkine, Raouf & Fabbri, Giorgio & Federico, Salvatore & Gozzi, Fausto, 2022. "A dynamic theory of spatial externalities," Games and Economic Behavior, Elsevier, vol. 132(C), pages 133-165.
    18. Camacho, Carmen & Pérez-Barahona, Agustín, 2015. "Land use dynamics and the environment," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 96-118.
    19. Bo Qin & Dongmei Zeng & Angang Gao, 2022. "Convergence effect of the Belt and Road Initiative on income disparity: evidence from China," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-16, December.
    20. William Brock & Anastasios Xepapadeas, 2020. "Spatial Environmental and Resource Economics," DEOS Working Papers 2002, Athens University of Economics and Business.

    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:hal:psewpa:hal-03693086. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.