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

David Desmarchelier, Magali Jaoul-Grammare (), Guillaume Morel and Thi Kim Cuong Pham ()
Additional contact information
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: 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
Thi Kim Cuong Pham: EconomiX - EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique

Working Papers from HAL

Abstract: This paper develops a competitive Ramsey-Cass-Koopmans framework in which an infectious disease evolves according to a simple SIS model. It aims at examining how the lockdown a§ects infectious disease persistence, individual welfare, and economic dynamics. In contrast to the existing literature, two types of infectives are introduced: (1) symptomatic and (2) asymptomatic. While the former is assumed to be too ill to work, the latter supply their labor and spread the disease. The government imposes a lockdown as an instrument to control the disease spread. In the long run, when the contamination rate of the disease is relatively high and the share of asymptomatics is low enough, the lockdown is welfare improving regardless of the degree of household empathy toward infectives. Moreover, 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.

Keywords: Bogdanov-Takens bifurcation; Hopf bifurcation; Lockdown; Ramsey model; SIS model (search for similar items in EconPapers)
Date: 2022
Note: View the original document on HAL open archive server: https://hal.science/hal-04159807
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-04159807/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04159807

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().