Modelagem Matemática para a Alocação de Leitos de UTI com Diferentes Tipos de Leitos e Taxa de Ocupação
Resumo
Este trabalho aborda um problema de alocação de leitos de Unidade de Terapia Intensiva (UTI), em que se considera diferentes tipos de leitos e uma taxa de ocupação ideal. Tal problema surge da dificuldade de profissionais da saúde em escolher quais pacientes alocar em leitos de UTI, devido à quantidade de fatores em consideração. Dessa forma, é proposta uma nova modelagem matemática que integra diferentes tipos de leitos e taxa de ocupação ideal, enquanto maximiza a taxa de sobrevivência dos pacientes. Para a validação do modelo, experimentos computacionais de simulação foram realizados a partir de dados reais do Hospital Universitário da Universidade Federal do Maranhão (HU-UFMA), e os resultados destacam a importância do modelo principalmente em situações de alta demanda.
Referências
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Frej, E. A., Roselli, L. R. P., Alberti, A. R., Britto, M. A., de Barros Campelo Júnior, E., Ferreira, R. J. P., and de Almeida, A. T. (2023). Collaborative decision model for allocating intensive care units beds with scarce resources in health systems: A portfolio based approach under expected utility theory and bayesian decision analysis. Mathematics, 11(3):659.
Frej, E. A., Roselli, L. R. P., Ferreira, R. J. P., Alberti, A. R., de Almeida, A. T., et al. (2021). Decision model for allocation of intensive care unit beds for suspected covid-19 patients under scarce resources. Computational and Mathematical Methods in Medicine, 2021.
Gurobi Optimization, L. (2023). Gurobi optimizer reference manual.
Karboub, K. and Tabaa, M. (2023). Bed allocation optimization based on survival analysis, treatment trajectory and costs estimations. IEEE Access.
King, M., Ramnarayan, P., Seaton, S. E., and Pagel, C. (2019). Modelling the allocation of paediatric intensive care retrieval teams in england and wales. Archives of Disease in Childhood, 104(10):962–966.
Murray, L. L., Wilson, J. A., Rodrigues, F. F., and Zaric, G. S. (2023). Forecasting icu census by combining time series and survival models. Critical Care Explorations.
Schmidt, F., Schmidt, F., Hauptmann, C., Hauptmann, C., Kohlenz, W., Kohlenz, W., Gasser, P., Gasser, P., Hartmann, S., Hartmann, S., Daunderer, M., Daunderer, M., Weiler, T., Weiler, T., Nowak, L., and Nowak, L. (2021). Tackling the waves of covid-19: A planning model for intrahospital resource allocation. Frontiers in Health Services.
Valeva, S., Pang, G., Schaefer, A. J., and Clermont, G. (2023). Acuity-based allocation of icu-downstream beds with flexible staffing. INFORMS journal on computing.
Wang, X. and Wang, L. (2008). A new mathematical model for analyzing cqi channel allocation mechanism in ieee 802.16 systems. In 2008 4th IEEE International Conference on Circuits and Systems for Communications, pages 177–181. IEEE.
White, D. B., White, D. B., Lo, B., and Lo, B. (2021). Promoting equity with a multiprinciple framework to allocate scarce icu resources. Journal of Medical Ethics.
Wolsey, L. A. (2020). Integer programming. John Wiley & Sons.
Craxì, L., Vergano, M., Savulescu, J., and Wilkinson, D. (2020). Rationing in a pandemic: lessons from italy. Asian Bioethics Review, 12:325–330.
Dantzig, G. B. (2002). Linear programming. Operations research, 50(1):42–47.
de Vicuña Bilbao, D. G. and de Vicuña Bilbao, D. G. (2022). Simulation models to support intensive care unit decision-making in pandemic and non-pandemic times. null.
Dieteren, C. M., van Hulsen, M. A., Rohde, K. I., and van Exel, J. (2022). How should icu beds be allocated during a crisis? evidence from the covid-19 pandemic. Plos one, 17(8):e0270996.
EBSERH (2022). Relatório gerencial dos HUFs 2019-2022. [link]. [online, acesso em 27-fevereiro-2024].
Frej, E. A., Roselli, L. R. P., Alberti, A. R., Britto, M. A., de Barros Campelo Júnior, E., Ferreira, R. J. P., and de Almeida, A. T. (2023). Collaborative decision model for allocating intensive care units beds with scarce resources in health systems: A portfolio based approach under expected utility theory and bayesian decision analysis. Mathematics, 11(3):659.
Frej, E. A., Roselli, L. R. P., Ferreira, R. J. P., Alberti, A. R., de Almeida, A. T., et al. (2021). Decision model for allocation of intensive care unit beds for suspected covid-19 patients under scarce resources. Computational and Mathematical Methods in Medicine, 2021.
Gurobi Optimization, L. (2023). Gurobi optimizer reference manual.
Karboub, K. and Tabaa, M. (2023). Bed allocation optimization based on survival analysis, treatment trajectory and costs estimations. IEEE Access.
King, M., Ramnarayan, P., Seaton, S. E., and Pagel, C. (2019). Modelling the allocation of paediatric intensive care retrieval teams in england and wales. Archives of Disease in Childhood, 104(10):962–966.
Murray, L. L., Wilson, J. A., Rodrigues, F. F., and Zaric, G. S. (2023). Forecasting icu census by combining time series and survival models. Critical Care Explorations.
Schmidt, F., Schmidt, F., Hauptmann, C., Hauptmann, C., Kohlenz, W., Kohlenz, W., Gasser, P., Gasser, P., Hartmann, S., Hartmann, S., Daunderer, M., Daunderer, M., Weiler, T., Weiler, T., Nowak, L., and Nowak, L. (2021). Tackling the waves of covid-19: A planning model for intrahospital resource allocation. Frontiers in Health Services.
Valeva, S., Pang, G., Schaefer, A. J., and Clermont, G. (2023). Acuity-based allocation of icu-downstream beds with flexible staffing. INFORMS journal on computing.
Wang, X. and Wang, L. (2008). A new mathematical model for analyzing cqi channel allocation mechanism in ieee 802.16 systems. In 2008 4th IEEE International Conference on Circuits and Systems for Communications, pages 177–181. IEEE.
White, D. B., White, D. B., Lo, B., and Lo, B. (2021). Promoting equity with a multiprinciple framework to allocate scarce icu resources. Journal of Medical Ethics.
Wolsey, L. A. (2020). Integer programming. John Wiley & Sons.
Publicado
25/06/2024
Como Citar
GOMES, Carlos Eduardo V.; CLÍMACO, Glaubos; CARVALHO, João Augusto F. Nunes de; QUINTANILHA, Darlan Bruno Pontes.
Modelagem Matemática para a Alocação de Leitos de UTI com Diferentes Tipos de Leitos e Taxa de Ocupação. In: SIMPÓSIO BRASILEIRO DE COMPUTAÇÃO APLICADA À SAÚDE (SBCAS), 24. , 2024, Goiânia/GO.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2024
.
p. 226-237.
ISSN 2763-8952.
DOI: https://doi.org/10.5753/sbcas.2024.2168.
