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Infectious disease and endogenous cycles: Lockdown hits two birds with one stone

Author

Listed:
  • David Desmarchelier

    (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Magali Jaoul-Grammare

    (BETA - Bureau d'Économie Théorique et Appliquée - AgroParisTech - UNISTRA - Université de Strasbourg - Université de Haute-Alsace (UHA) - Université de Haute-Alsace (UHA) Mulhouse - Colmar - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Guillaume Morel

    (Umeå University = Umeå Universitet)

  • Thi Pham

    (EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper develops a competitive Ramsey–Cass–Koopmans framework in which an infectious disease is considered. A lockdown is introduced to control the disease spread. Considering the dynamics, a stable limit cycle can emerge near the endemic steady‐state, through a Hopf bifurcation, when the share of infectives increases sufficiently the marginal utility of consumption. Particularly, we prove that it is possible to tune the lockdown to simultaneously obtain the limit cycle disappearance and the disease eradication (Bogdanov–Takens bifurcation). In this sense, the lockdown allows hitting two birds with one stone .

Suggested Citation

  • David Desmarchelier & Magali Jaoul-Grammare & Guillaume Morel & Thi Pham, 2025. "Infectious disease and endogenous cycles: Lockdown hits two birds with one stone," Post-Print halshs-05419099, HAL.
    • Handle: RePEc:hal:journl:halshs-05419099
    DOI: 10.1111/ijet.70001
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-05419099v1
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