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SIR Economic Epidemiological Models with Disease Induced Mortality

Author

Listed:
  • Aditya Goenka
  • Lin Liu
  • Manh-Hung Nguyen
Abstract
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.

Suggested Citation

  • Aditya Goenka & Lin Liu & Manh-Hung Nguyen, 2021. "SIR Economic Epidemiological Models with Disease Induced Mortality," Working Papers 202103, University of Liverpool, Department of Economics.
    • Handle: RePEc:liv:livedp:202103
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    Cited by:

    1. Luca Gori & Cristiana Mammana & Piero Manfredi & Elisabetta Michetti, 2022. "Economic development with deadly communicable diseases and public prevention," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 912-943, October.
    2. Guimarães, Luís, 2021. "Antibody tests: They are more important than we thought," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    3. Hai-Anh Dang & Toan L.D. Huynh & Manh-Hung Nguyen, 2023. "Does the COVID-19 pandemic disproportionately affect the poor? Evidence from a six-country survey," Journal of Economics and Development, Emerald Group Publishing Limited, vol. 26(1), pages 2-18, December.
    4. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2021. "COVID-19 and a Green Recovery?," Economic Modelling, Elsevier, vol. 104(C).
    5. Goenka, Aditya & Liu, Lin & Nguyen, Manh-Hung, 2021. "Modeling optimal quarantines with waning immunity," TSE Working Papers 21-1206, Toulouse School of Economics (TSE), revised Jul 2022.
    6. Caulkins, Jonathan P. & Grass, Dieter & Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Prskawetz, Alexia & Seidl, Andrea & Wrzaczek, Stefan, 2021. "The optimal lockdown intensity for COVID-19," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    7. Cui Zhang & Dandan Zhang, 2023. "Spatial Interactions and the Spread of COVID-19: A Network Perspective," Computational Economics, Springer;Society for Computational Economics, vol. 62(1), pages 383-405, June.
    8. Jacek Rothert, 2021. "Optimal federal transfers during uncoordinated response to a pandemic," GRAPE Working Papers 58, GRAPE Group for Research in Applied Economics.
    9. Cozzi, Guido & Galli, Silvia, 2022. "Covid-19 Vaccines, Innovation, and Intellectual Property Rights," GLO Discussion Paper Series 1095, Global Labor Organization (GLO).
    10. Carmona, Julio & León, ángel, 2021. "Pandemic Effects in the Solow Growth Model," QM&ET Working Papers 21-1, University of Alicante, D. Quantitative Methods and Economic Theory, revised 07 Apr 2022.
    11. Jacek Rothert, 2022. "Optimal federal transfers during uncoordinated response to a pandemic," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1124-1153, October.
    12. Carmona, Julio, 2024. "Using the Solow Growth Model. The Impact of Endemic Diseases on Economic Growth," QM&ET Working Papers 24-1, University of Alicante, D. Quantitative Methods and Economic Theory.
    13. Michael Freiberger & Dieter Grass & Michael Kuhn & Andrea Seidl & Stefan Wrzaczek, 2022. "Chasing up and locking down the virus: Optimal pandemic interventions within a network," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1182-1217, October.
    14. Carmona, Julio, 2022. "A Simple Endemic Growth Model for Undergraduates," QM&ET Working Papers 22-1, University of Alicante, D. Quantitative Methods and Economic Theory, revised 03 Mar 2022.
    15. Sharbayta, Sileshi Sintayehu & Buonomo, Bruno & d'Onofrio, Alberto & Abdi, Tadesse, 2022. "‘Period doubling’ induced by optimal control in a behavioral SIR epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    16. Vahdani, Behnam & Mohammadi, Mehrdad & Thevenin, Simon & Meyer, Patrick & Dolgui, Alexandre, 2023. "Production-sharing of critical resources with dynamic demand under pandemic situation: The COVID-19 pandemic," Omega, Elsevier, vol. 120(C).
    17. Zachariah Sinkala & Vajira Manathunga & Bichaka Fayissa, 2022. "An Epidemic Compartment Model for Economic Policy Directions for Managing Future Pandemic," Papers 2202.05374, arXiv.org.

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    More about this item

    Keywords

    Infectious diseases; Covid-19; SIR model; mortality; sufficiency condi-tions; economic growth; lockdown; prevention; health expenditure;
    All these keywords.

    JEL classification:

    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I10 - Health, Education, and Welfare - - Health - - - General
    • I15 - Health, Education, and Welfare - - Health - - - Health and Economic Development
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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