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Stochastic models for geriatric in-patient behaviour

V Irvine1, S McClean, P Millard

  • 1Department of Mathematics, University of Ulster, Coleraine, Northern Ireland.

IMA Journal of Mathematics Applied in Medicine and Biology
|January 1, 1994
PubMed
Summary

This study introduces a new Markov model for geriatric medicine patient flow, differentiating between acute/rehabilitative and long-stay care. This model improves hospital planning by accounting for patient heterogeneity and providing better resource management insights.

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Area of Science:

  • Geriatric Medicine
  • Health Services Research
  • Mathematical Modeling

Background:

  • Geriatric medicine departments manage distinct patient populations: acute/rehabilitative and long-stay.
  • These patient groups have different organizational and resource requirements.
  • Existing hospital planning models fail to account for patient heterogeneity, leading to inefficiencies.

Purpose of the Study:

  • To develop and evaluate a two-stage continuous-time Markov model for patient movement in geriatric hospitals.
  • To address the limitations of current models by incorporating patient heterogeneity.
  • To provide a more accurate method for estimating the number of geriatric patients requiring hospital care.

Main Methods:

  • A two-stage continuous-time Markov model was employed, with stages representing acute/rehabilitative and long-stay patients.

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  • Patient transitions between stages, departures (death/discharge), and admissions were modeled.
  • Admissions were considered as either replacements for departures or as a Poisson stream.
  • Model expressions for patient number distributions and movements were derived and tested using hospital data.

    • Main Results:

    • The model successfully describes patient movement through distinct geriatric care stages.
    • It accounts for patient heterogeneity, unlike previous simplistic models.
    • The approach allows for the estimation of both means and variances in patient numbers, enhancing planning accuracy.

    Conclusions:

    • The proposed Markov model offers a more sophisticated and accurate approach to understanding and managing patient flow in geriatric medicine.
    • This enhanced modeling capability can lead to improved hospital resource allocation and patient care planning.
    • The model's ability to capture patient variability provides valuable insights for healthcare administrators and policymakers.