SIR economic epidemiological models with disease induced mortality

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  • University of Liverpool
  • University of Toulouse


This paper studies an optimal growth model where there is an infectious disease with SIR dynamics which can lead to mortality. Health expenditures (alternatively intensity of lockdowns) can be made to reduce infectivity of the disease. We study implications of two different ways to model the disease related mortality – early and late in infection mortality – on the equilibrium health and economic outcomes. In the former, increasing mortality reduces infections by decreasing the fraction of infectives in the population, while in the latter the fraction of infectives increases. We characterize the steady states and the outcomes depend in the way mortality is modeled. With early mortality, increasing mortality leads to higher equilibrium per capita output and consumption while in the late mortality model these decrease. We establish sufficiency conditions and provide the first results in economic models with SIR dynamics with and without disease related mortality — a class of models which are non-convex and have endogenous discounting so that no existing results are applicable.

Bibliographic note

Funding Information: We thank the referees for their helpful comments. The usual disclaimer applies. Manh-Hung Nguyen acknowledges support from ANR, France under grant ANR-17-EURE-0010 (Investissements d’Avenir program). Publisher Copyright: © 2021 Elsevier B.V.


Original languageEnglish
Article number102476
Number of pages16
JournalJournal of Mathematical Economics
Early online date2 Feb 2021
Publication statusPublished - Mar 2021


  • Covid-19, Infectious diseases, Lockdown, Mortality, SIR model, Sufficiency conditions

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