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Modeling medical material shortage using Markov processes

Author

Listed:
  • Alexis Roussel

    (Université de Franche-Comté, CRESE, F-25000 Besançon, France)

  • Romain Biard

    (Université de Franche-Comté, LMB UMR 6623, F-25000 Besançon, France)

  • Marc Deschamps

    (Université de Franche-Comté, CRESE, F-25000 Besançon, France)

  • Mostapha Diss

    (Université de Franche-Comté, CRESE, F-25000 Besançon, France)

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 ex- act 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

  • Alexis Roussel & Romain Biard & Marc Deschamps & Mostapha Diss, 2023. "Modeling medical material shortage using Markov processes," Working Papers 2023-04, CRESE.
    • Handle: RePEc:crb:wpaper:2023-04
    as

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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.
    3. 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).
    4. 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.
    5. 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.
    6. Andrew Atkeson, 2020. "What Will Be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios," NBER Working Papers 26867, National Bureau of Economic Research, Inc.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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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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