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

Author

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  • 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 nationale des ponts et chaussées - 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," Working Papers hal-03693086, HAL.
    • Handle: RePEc:hal:wpaper:hal-03693086
    Note: View the original document on HAL open archive server: https://hal.science/hal-03693086v1
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    References listed on IDEAS

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    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. Bosi, Stefano & Camacho, Carmen & Desmarchelier, David, 2021. "Optimal lockdown in altruistic economies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    3. Desbordes, Rodolphe, 2021. "Spatial dynamics of major infectious diseases outbreaks: A global empirical assessment," 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.
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