Working Paper BETA #2021-23

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

Author(s) : David Desmarchelier, Magali Jaoul-Grammare, Guillaume Morel, Thi Kim Cuong Pham

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) symptomatics and (2) asymptomatics. While the former is assumed to be too ill to work, the latter supply their labour 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.

Key-words : Bogdanov-Takens bifurcation, Hopf bifurcation, Lockdown, Ramsey model, SIS model.

JEL Classification : C61, E13, I18, O41.