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A time-space integro-differential economic model of epidemic control

Author

Listed:
  • Carmen Camacho

    (Paris School of Economics and CNRS)

  • Rodolphe Desbordes

    (Campus Grand Paris)

  • Davide Torre

    (Sophia Antipolis Campus)

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 local diffusion effect, a temporal effect, and a global diffusion 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 the finite horizon case in detail and we provide the closed-form expression of the optimal policy to be implemented to control the epidemic while sustaining economic growth. We also propose two different extensions: The first one considers an infinite horizon model while, the second one, is related to a multi-period framework.

Suggested Citation

  • Carmen Camacho & Rodolphe Desbordes & Davide Torre, 2024. "A time-space integro-differential economic model of epidemic control," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 307-348, February.
    • Handle: RePEc:spr:joecth:v:77:y:2024:i:1:d:10.1007_s00199-023-01506-z
    DOI: 10.1007/s00199-023-01506-z
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    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.

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    More about this item

    Keywords

    Epidemics; Macroeconomic outcomes; Mitigation policies;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
    • I10 - Health, Education, and Welfare - - Health - - - General

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