David Desmarchelier, Magali Jaoul-Grammare, Guillaume Morel, Thi K. C. Pham
{"title":"Infectious disease and endogenous cycles: Lockdown hits two birds with one stone","authors":"David Desmarchelier, Magali Jaoul-Grammare, Guillaume Morel, Thi K. C. Pham","doi":"10.1111/ijet.70001","DOIUrl":null,"url":null,"abstract":"<p>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 <i>hitting two birds with one stone</i>.</p>","PeriodicalId":44551,"journal":{"name":"International Journal of Economic Theory","volume":"21 3","pages":"316-342"},"PeriodicalIF":0.7000,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Economic Theory","FirstCategoryId":"96","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/ijet.70001","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
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.