IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-04222226.html
   My bibliography  Save this paper

Modeling medical material shortage using Markov processes

Author

Listed:
  • Romain Biard

    (LMB - Laboratoire de Mathématiques de Besançon (UMR 6623) - CNRS - Centre National de la Recherche Scientifique - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Marc Deschamps

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Mostapha Diss

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Alexis Roussel

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

Abstract

The management and allocation of health resources, in particular equipment such as ventilators, has been the object of significant interest by a health community that is concerned to avoid new shortages. In this article, we develop a Markov chain based model considering random arrivals and discharges of patients in an intensive care unit requiring ventilator support. We provide a methodology in order to compute the exact probability distribution of the time-shortage, which is the moment where no more ventilators are available. We propose two applications of this model: a preventive traffic signal and a tool to evaluate purchasing decisions. A calibration of parameters based on real empirical data from a French hospital is carried out in order to test the operational use of the model.

Suggested Citation

  • Romain Biard & Marc Deschamps & Mostapha Diss & Alexis Roussel, 2023. "Modeling medical material shortage using Markov processes," Working Papers hal-04222226, HAL.
    • Handle: RePEc:hal:wpaper:hal-04222226
    Note: View the original document on HAL open archive server: https://hal.science/hal-04222226
    as

    Download full text from publisher

    File URL: https://hal.science/hal-04222226/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Parag A. Pathak & Tayfun Sönmez & M. Utku Unver & M. Bumin Yenmez, 2020. "Leaving No Ethical Value Behind: Triage Protocol Design for Pandemic Rationing," NBER Working Papers 26951, National Bureau of Economic Research, Inc.
    2. Daron Acemoglu & Victor Chernozhukov & Ivàn Werning & Michael D. Whinston, 2020. "A Multi-Risk SIR Model with Optimally Targeted Lockdown," CeMMAP working papers CWP14/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐Baptiste Tondji, 2022. "Vaccine and inclusion," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1101-1123, October.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
    4. Hyun-Rok Lee & Taesik Lee, 2018. "Markov decision process model for patient admission decision at an emergency department under a surge demand," Flexible Services and Manufacturing Journal, Springer, vol. 30(1), pages 98-122, June.
    5. L. Mayhew & D. Smith, 2008. "Using queuing theory to analyse the Government’s 4-h completion time target in Accident and Emergency departments," Health Care Management Science, Springer, vol. 11(1), pages 11-21, March.
    6. Andrew Atkeson, 2020. "What Will be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios," Staff Report 595, Federal Reserve Bank of Minneapolis.
    7. Bonneuil, Noël, 2021. "Optimal age- and sex-based management of the queue to ventilators during the Covid-19 crisis," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ichino, Andrea & Favero, Carlo A. & Rustichini, Aldo, 2020. "Restarting the economy while saving lives under Covid-19," CEPR Discussion Papers 14664, C.E.P.R. Discussion Papers.
    2. Terrence Iverson & Edward Barbier, 2021. "National and Sub-National Social Distancing Responses to COVID-19," Economies, MDPI, vol. 9(2), pages 1-15, May.
    3. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Epidemics and macroeconomic outcomes: Social distancing intensity and duration," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    4. Jesper Akesson & Sam Ashworth-Hayes & Robert Hahn & Robert Metcalfe & Itzhak Rasooly, 2022. "Fatalism, beliefs, and behaviors during the COVID-19 pandemic," Journal of Risk and Uncertainty, Springer, vol. 64(2), pages 147-190, April.
    5. Giorgio Fabbri & Salvatore Federico & Davide Fiaschi & Fausto Gozzi, 2024. "Mobility decisions, economic dynamics and epidemic," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(1), pages 495-531, February.
    6. Lin William Cong & Ke Tang & Bing Wang & Jingyuan Wang, 2021. "An AI-assisted Economic Model of Endogenous Mobility and Infectious Diseases: The Case of COVID-19 in the United States," Papers 2109.10009, arXiv.org.
    7. Timo Boppart & Karl Harmenberg & John Hassler & Per Krusell & Jonna Olsson, 2020. "Integrated Epi-Econ Assessment," NBER Working Papers 28282, National Bureau of Economic Research, Inc.
    8. Mellacher, Patrick, 2020. "COVID-Town: An Integrated Economic-Epidemiological Agent-Based Model," MPRA Paper 103661, University Library of Munich, Germany.
    9. Bosi, Stefano & Camacho, Carmen & Desmarchelier, David, 2021. "Optimal lockdown in altruistic economies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    10. Garriga, Carlos & Manuelli, Rody & Sanghi, Siddhartha, 2022. "Optimal management of an epidemic: Lockdown, vaccine and value of life," Journal of Economic Dynamics and Control, Elsevier, vol. 140(C).
    11. Thomas Kruse & Philipp Strack, 2020. "Optimal Control of an Epidemic through Social Distancing," Cowles Foundation Discussion Papers 2229R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2020.
    12. Çakmaklı, Cem & Demiralp, Selva & Özcan, Şebnem Kalemli & Yeşiltaş, Sevcan & Yıldırım, Muhammed A., 2023. "COVID-19 and emerging markets: A SIR model, demand shocks and capital flows," Journal of International Economics, Elsevier, vol. 145(C).
    13. Bonadio, Barthélémy & Huo, Zhen & Levchenko, Andrei A. & Pandalai-Nayar, Nitya, 2021. "Global supply chains in the pandemic," Journal of International Economics, Elsevier, vol. 133(C).
    14. Michael Barnett & Greg Buchak & Constantine Yannelis, 2023. "Epidemic responses under uncertainty," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 120(2), pages 2208111120-, January.
    15. Shouyong Shi, 2023. "Knowledge, Germs and Output," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 48, pages 297-319, April.
    16. Emanuele Colombo Azimonti & Luca Portoghese & Patrizio Tirelli, 2022. "Covid-19 supply-side fiscal policies to escape the health-vs-economy dilemma," DEM Working Papers Series 208, University of Pavia, Department of Economics and Management.
    17. Camacho, Carmen & Vasilakis, Chrysovalantis, 2023. "Transmissible Diseases, Vaccination and Inequality," IZA Discussion Papers 16504, Institute of Labor Economics (IZA).
    18. Stefano Bosi & Carmen Camacho & David Desmarchelier, 2020. "Optimal lockdown in altruistic economies," PSE Working Papers halshs-02652165, HAL.
    19. Enrique G. Mendoza & Eugenio Rojas & Linda L. Tesar & Jing Zhang, 2023. "A Macroeconomic Model of Healthcare Saturation, Inequality and the Output–Pandemia Trade-off," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 71(1), pages 243-299, March.
    20. Victor Aguirregabiria & Jiaying Gu & Yao Luo & Pedro Mira, 2020. "A Dynamic Structural Model of Virus Diffusion and Network Production: A First Report," Working Papers tecipa-665, University of Toronto, Department of Economics.

    More about this item

    Keywords

    Intensive care unit; ventilator shortage; Markov process; traffic signal; purchasing management.;
    All these keywords.

    JEL classification:

    • I10 - Health, Education, and Welfare - - Health - - - General
    • I19 - Health, Education, and Welfare - - Health - - - Other
    • C0 - Mathematical and Quantitative Methods - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-04222226. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.