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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-04222226v1
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    References listed on IDEAS

    as
    1. 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.
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      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean-Baptiste Tondji, 2022. "Vaccine and Inclusion," Working Papers 2202E Classification-C62,, University of Ottawa, Department of Economics.
      • Zéphirin Nganmeni & Roland Pongou & Bertrand Tchantcho & Jean‐baptiste Tondji, 2022. "Vaccine and inclusion," Post-Print hal-04257703, HAL.
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    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

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