Estratégias para Alocação de Recursos de Controle Ótimo em Cenários Estocásticos
Resumo
A aplicação de modelos computacionais à epidemiologia tem contribuído para o entendimento da dinâmica de várias doenças infecciosas. Tais modelos estão sendo usados para simulações e predições em várias políticas de saúde pública contra a atual pandemia do COVID-19. Três exemplos amplamente utilizados são formulações determinísticas dos modelos compartimentais, baseados em indivíduos e baseados em redes complexas. Neste contexto, este trabalho propõe estudos sobre uma perspectiva estocástica destes modelos no intuito de inserir incerteza à dinâmica epidemiológica, bem como a obtenção de estratégias de controle ótimo para sua mitigação. Os resultados mostram reduções significativas na quantidade de indivíduos infectados.
Referências
Anderson, R. M. and May, R. M. (1992). Infectious diseases of humans: Dinamics and control. Oxford University Press.
Bastos, S. B. and Cajueiro, D. O. (2020). Modeling and forecasting the covid-19 pandemic in brazil. arXiv preprint arXiv:2003.14288.
Biswas, K. and Sen, P. (2020). Space-time dependence of corona virus (covid-19) outbreak. arXiv preprint arXiv:2003.03149.
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., and Hwang, D.-U. (2006). Complex networks: Structure and dynamics. Physics reports, 424(4):175–308.
Casagrandi, R., Bolzoni, L., Levin, S. A., and Andreasen, V. (2006). The sirc model and influenza a. Mathematical Biosciences, 200:156–169.
Chang, S. L., Harding, N., Zachreson, C., Cliff, O. M., and Prokopenko, M. (2020). Modelling transmission and control of the covid-19 pandemic in australia. arXiv preprint arXiv:2003.10218.
Choisy, M., Guégan, and Rohani, P. (2007). Mathematical Modeling of Infectious Diseases Dynamics. ENCYCLOPEDIA OF INFECTIOUS DISEASES: MODERN METHODOLOGIES.
Cisternas, J., Gear, C. W., Levin, S., and Kevrekidis, I. G. (2004). Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 460(2050):2761–2779.
Di Giamberardino, P. and Iacoviello, D. (2019). A linear quadratic regulator for nonlinear sirc epidemic model. In 2019 23rd International Conference on System Theory, Control and Computing (ICSTCC), pages 733–738. IEEE.
Emilia, V. and White, R. (2010). An Introduction to Infectious Disease Modelling. Oxford University Press.
Filho, N. A. and Rouquayrol, M. Z. (2006). Introdução à epidemiologia. Guanabara Koogan.
Galv˜ao Filho, A. R., de Lima, T. W., da Silva Soares, A., and Coelho, C. J. (2017). A stochastic approach of sirc model using individual-based epidemiological models. In EPIA Conference on Artificial Intelligence, pages 778–788. Springer.
Galv˜ao Filho, A. R., Galv˜ao, R. K. H., and Yoneyama, T. (2013). Otimização da alocação temporal de recursos para combate a epidemias com transmiss˜ao sazonal através de métodos de barreira. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 1(1).
Galv˜ao Filho, A. R., Martins de Paula, L. C., Coelho, C. J., de Lima, T. W., and da Silva Soares, A. (2016). Cuda parallel programming for simulation of epidemiological models based on individuals. Mathematical Methods in the Applied Sciences, 39(3):405–411.
Galvão Filho, A. R., Arruda, F. D. B., Galvão, R. K. H., and Yoneyama, T. (2011). Programação paralela CUDA para simulação de modelos epidemiológicos baseados em indivíduos. In Em: Anais do X Simpósio Brasileiro de Automação Inteligente, São João del-Rei, MG.
Kermack, W. and Mckendrick, A. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London - Series A, 115:700 – 721.
Lambert, S., Gilot-Fromont, E., To¨ıgo, C., Marchand, P., Petit, E., Garin-Bastuji, B., Gauthier, D., Gaillard, J.-M., Rossi, S., and Thébault, A. (2020). An individual-based model to assess the spatial and individual heterogeneity of brucella melitensis transmission in alpine ibex. Ecological Modelling, 425:109009.
Luenberger, D. G. (2010). Introduction to Dynamic Systems Theory, Models, and Applications. Oxford University Press.
Molter, A., Piovesan, L., Pergher, R., and Varriale, M. (2016). Controle O´ timo em epidemias de dengue. Tema, 17(2).
Nowzari, C., Preciado, V. M., and Pappas, G. J. (2016). Analysis and control of epidemics: A survey of spreading processes on complex networks. IEEE Control Systems, 36(1):26–46.
Perez, I. A., Trunfio, P. A., La Rocca, C. E., and Braunstein, L. A. (2019). Controlling distant contacts to reduce disease spreading on disordered complex networks. Physica A: Statistical Mechanics and its Applications, page 123709.
Siettos, C. I. and Russo, L. (2013). Mathematical modeling of infectious disease dynamics. Mathematical modeling of infectious disease dynamics, 4(4).
Yi-Chia, W., Ching-Sunga, C., and Yu-Jiuna, C. (2020). The outbreak of covid-19 an overview. Journal of the Chinese Medical Association, 83(3).
Bastos, S. B. and Cajueiro, D. O. (2020). Modeling and forecasting the covid-19 pandemic in brazil. arXiv preprint arXiv:2003.14288.
Biswas, K. and Sen, P. (2020). Space-time dependence of corona virus (covid-19) outbreak. arXiv preprint arXiv:2003.03149.
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., and Hwang, D.-U. (2006). Complex networks: Structure and dynamics. Physics reports, 424(4):175–308.
Casagrandi, R., Bolzoni, L., Levin, S. A., and Andreasen, V. (2006). The sirc model and influenza a. Mathematical Biosciences, 200:156–169.
Chang, S. L., Harding, N., Zachreson, C., Cliff, O. M., and Prokopenko, M. (2020). Modelling transmission and control of the covid-19 pandemic in australia. arXiv preprint arXiv:2003.10218.
Choisy, M., Guégan, and Rohani, P. (2007). Mathematical Modeling of Infectious Diseases Dynamics. ENCYCLOPEDIA OF INFECTIOUS DISEASES: MODERN METHODOLOGIES.
Cisternas, J., Gear, C. W., Levin, S., and Kevrekidis, I. G. (2004). Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 460(2050):2761–2779.
Di Giamberardino, P. and Iacoviello, D. (2019). A linear quadratic regulator for nonlinear sirc epidemic model. In 2019 23rd International Conference on System Theory, Control and Computing (ICSTCC), pages 733–738. IEEE.
Emilia, V. and White, R. (2010). An Introduction to Infectious Disease Modelling. Oxford University Press.
Filho, N. A. and Rouquayrol, M. Z. (2006). Introdução à epidemiologia. Guanabara Koogan.
Galv˜ao Filho, A. R., de Lima, T. W., da Silva Soares, A., and Coelho, C. J. (2017). A stochastic approach of sirc model using individual-based epidemiological models. In EPIA Conference on Artificial Intelligence, pages 778–788. Springer.
Galv˜ao Filho, A. R., Galv˜ao, R. K. H., and Yoneyama, T. (2013). Otimização da alocação temporal de recursos para combate a epidemias com transmiss˜ao sazonal através de métodos de barreira. Proceeding Series of the Brazilian Society of Computational and Applied Mathematics, 1(1).
Galv˜ao Filho, A. R., Martins de Paula, L. C., Coelho, C. J., de Lima, T. W., and da Silva Soares, A. (2016). Cuda parallel programming for simulation of epidemiological models based on individuals. Mathematical Methods in the Applied Sciences, 39(3):405–411.
Galvão Filho, A. R., Arruda, F. D. B., Galvão, R. K. H., and Yoneyama, T. (2011). Programação paralela CUDA para simulação de modelos epidemiológicos baseados em indivíduos. In Em: Anais do X Simpósio Brasileiro de Automação Inteligente, São João del-Rei, MG.
Kermack, W. and Mckendrick, A. (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London - Series A, 115:700 – 721.
Lambert, S., Gilot-Fromont, E., To¨ıgo, C., Marchand, P., Petit, E., Garin-Bastuji, B., Gauthier, D., Gaillard, J.-M., Rossi, S., and Thébault, A. (2020). An individual-based model to assess the spatial and individual heterogeneity of brucella melitensis transmission in alpine ibex. Ecological Modelling, 425:109009.
Luenberger, D. G. (2010). Introduction to Dynamic Systems Theory, Models, and Applications. Oxford University Press.
Molter, A., Piovesan, L., Pergher, R., and Varriale, M. (2016). Controle O´ timo em epidemias de dengue. Tema, 17(2).
Nowzari, C., Preciado, V. M., and Pappas, G. J. (2016). Analysis and control of epidemics: A survey of spreading processes on complex networks. IEEE Control Systems, 36(1):26–46.
Perez, I. A., Trunfio, P. A., La Rocca, C. E., and Braunstein, L. A. (2019). Controlling distant contacts to reduce disease spreading on disordered complex networks. Physica A: Statistical Mechanics and its Applications, page 123709.
Siettos, C. I. and Russo, L. (2013). Mathematical modeling of infectious disease dynamics. Mathematical modeling of infectious disease dynamics, 4(4).
Yi-Chia, W., Ching-Sunga, C., and Yu-Jiuna, C. (2020). The outbreak of covid-19 an overview. Journal of the Chinese Medical Association, 83(3).
Publicado
15/09/2020
Como Citar
GALVÃO FILHO, Arlindo R.; SOARES, Telma W. L.; COELHO, Clarimar J..
Estratégias para Alocação de Recursos de Controle Ótimo em Cenários Estocásticos. In: CONCURSO DE TESES E DISSERTAÇÕES - SIMPÓSIO BRASILEIRO DE COMPUTAÇÃO APLICADA À SAÚDE (SBCAS), 20. , 2020, Evento Online.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2020
.
p. 19-24.
ISSN 2763-8987.
DOI: https://doi.org/10.5753/sbcas.2020.11552.
