Autômatos celulares: melhorias de controlo e imunidade na simulação de fenômenos propagativos
DOI:
https://doi.org/10.18046/syt.v13i35.2149Palavras-chave:
Autômato celular, propagação epidémica, modelo SIR de recuperação da influenza AH1NX.Resumo
Os autômatos celulares bidimensionais são uma poderosa
ferramenta para a simulação de sistemas discretos complexos,
são úteis no tratamento de fenômenos propagativos tais
como epidemias ou incêndios. Este artigo propõe uma série de
melhorias teóricas, funcionais e aplicáveis ao estudo publicado
em 2009 por Hoya, Martin del Rey e Rodriguez, especificamente
destinadas a controlar os padrões de dispersão em autômatos
celulares com reticulados homogêneos de tamanho variável,
permitindo a simulação de conjuntos de células imunes que
agem como barreiras nos ambientes estudados. Como agente
propagante foi utilizado o modelo epidemiológico Suscetível-Infectado-
Recuperado [SIR] de recuperação da influenza tipo A.
O trabalho foi desenvolvido usando MATLAB®, resultando em
simulações mais realistas e versáteis, que parecem caber mais
fielmente às observações realizadas em padrões conhecidos de
influenza.
Referências
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Arenas, A. J., González-Parra, G., & Moraño, J. A. (2009). Stochastic modeling of the transmission of respiratory syncytial virus (RSV) in the region of Valencia, Spain. Biosys, 96(3), 206-212.
Beauchemina, C., Samuelb, J. & Tuszynskia, J. (2005). A simple cellular automaton model for influenza A viral infections. Journal of Theoretical Biology 232, 223-234.
Burniaková, L. (2007). The mathematics of infectious diseases [master thesis]. Comenius University: Bratislava, Eslovaquia. Retrieved from: http://diplomovka.sme.sk/zdroj/3138.pdf
Chowell, G., Ammon, C., Hengartner, N., & Hyman, J. (2006). Transmission dynamics of the great influenza pandemic of 1918 in
Geneva, Switzerland: Assessing the effects of hypothetical interventions. Journal of Theoretical Biology, 241(2), 93-204). Available at: http://math.lanl.gov/~mac/papers/bio/GAHH06b.pdf
Coburn, B., Wagner, B., & Blower, S. (2009) Modeling epidemics and pandemics: Insights into the future of swine flu (H1N1). BMC Medicine, 7. doi:10.1186/1741-7015-7-30 Available at: http://www.biomedcentral.com/content/pdf/1741-7015-7-30.pdf
Cuesta, H., Trueba, A., & Ruiz J. (2012). Autómata Celular Estocástico paralelizado por GPU aplicado a la simulación de enfermedades infecciosas en grandes poblaciones. Acta Universitaria, 22(6), 16-19. Available at: http://www.actauniversitaria.ugto.mx/index.php/acta/article/viewFile/356/pdf
Cunha, B. (2004). Influenza: Historical aspects of epidemics and pandemics. Infectious Disease Clinics of North America, 18(1), 148-155.
Doracelli, H. & Ospina, J. (2007). Bases para la modelación de epidemias: el Caso del síndrome respiratorio agudo severo en Canadá. Revista Salud Pública, 9(1), 121-123.
Dubacq, J.-C., Durand, B., & Formenti, E. (2001). Kolmogorov complexity and cellular automata classification. Theoretical Computer Science, 259(1), 271-285. doi:10.1016/S0304-3975(00)00012-8
Firestone, S., Cogger, N., Ward, M., Toribio, J., Moloney, B., & Dhand, N. (2012). The Influence of meteorology on the spread of influenza: Survival analysis of an equine influenza (A/H3N8) Outbreak. PloS One, 7(4). e35284. doi: 10.1371/journal.pone.0035284
Fonseca, F. & Blanco, W. (2010). Mecánica estadística de redes y propagación de enfermedades infecciosas. Revista Colombiana de Física, 42(3), 322-323. Available at: http://revcolfis.org/ojs/index.php/rcf/article/viewArticle/420316
Ganguly, N., Sikdar, B., Deutsch, A., Canright, G., & Chaudhuri (2003). A survey on cellular automata. Retrieved from: http://www.cs.unibo.it/bison/publications/CAsurvey.pdf
Gharib-Zahedi, R. M. & Ghaemi, M. (2012). Kinetics of hepatitis B virus infection: A cellular automaton model study. Journal of Paramedical Sciences, 3(3). Retrieved from: http://journals.sbmu.ac.ir/jps/article/download/3482/3130
Gómez, G. & Vargas-De-León, C. (2012). Modeling control strategies for influenza A H1N1 epidemics: SIR models. Revista Mexicana de Física, S58(1), 37-43. Available at: http://rmf.fciencias.unam.mx/~raem/caos/SC-7_1.pdf
Hauska, H. & Linde, A. (2008). The Russian influenza in Sweden in 1889-90: An example of geographic information system analysis. Eurosurveillance, 13(49). Retrieved from: http://www.ncbi.nlm.nih.gov/pubmed/19081003
Hoya, S., Martin del Rey, A. & Rodríguez, G. (2009). Using cellular automata to simulate epidemic diseases. Applied Mathematical Sciences, 3(20), 959-968. Available at: http://www.m-hikari.com/ams/ams-password-2009/ams-password17-20-2009/delreyAMS17-20-2009.pdf
Knipl, D. & Rӧst, G. (2011). Influenza models with wolfram mathematica [blog - Interesting mathematical problems in sciences and everyday life - 2011]. Retrieved from: http://www.model.u-szeged.hu/etc/edoc/imp/GRost/GRost.pdf
Lahoz-Beltrá, R. (2004). Bioinformática: simulación, vida artificial e inteligencia artificial. Madrid, España: Díaz de Santos.
Madrigal, J., Muñoz, L.A., & Garcia, M.J. (2011). Autómatas celulares en redes de Boltzmann [paper in VIII Congreso Colombiano de Métodos Numéricos: Simulación en Ciencias y Aplicaciones Industriales 8CCMN – 2011, Agosto. 10-12, 2011, Medellín, Colombia, Universidad EAFIT]. Retrieved from: http://mecanica.eafit.edu.co/8ccmn/articulos/Madrigal-8ccmn2011.pdf
Martin, O., Odlyzko, A., Wolfram, S. (1984). Algebraic properties of cellular automata. Communications in mathematical physics, 93(2), 219-258. Available at: http://www.stephenwolfram.com/publications/academic/algebraic-properties-cellular-automata.pdf
Martin-del-Rey, A. (2009). Epidemiologia matemática usando autómatas celulares sobre grafos. In XXI Congreso de Ecuaciones Diferenciales y Aplicaciones / XI Congreso de Matemática Aplicada [Actas del Cyda]. Retrieved from: http://matematicas.uclm.es/cedya09/archive/textos/35_Martin-del-Rey-A.pdf
Mendes-dos-Santos, L. & Silva-de.Souza, F. (2012). Uma análise do modelo SIR aplicado ao estudo da influenza A. In CEMAC Nordeste 2012, (pp.20-23). Retrieved from: http://www.sbmac.org.br/cmacs/cmac-ne/2012/trabalhos/PDF/113.pdf
Mitchell, M., Hraber, P. & Crutchfield, J. (1993). Revisiting the edge of chaos: Evolving cellular automata to perform computations [Report No. SFI Working Paper 93-03-014]. Retrieved from: http://arxiv.org/pdf/adap-org/9303003.pdf
Morse, S. (1995). Factors in the emergence of infectious diseases. Emerging Infectious Diseases, 1(1), 7-15. Available at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2626828/pdf/8903148.pdf
Ramasco, J. (2012). Predicción de los patrones de propagación de contacto con ordenadores. Medicina Balear, 28(1), 41-47. Available at: http://www.imbiomed.com.mx/1/1/articulos.php?method=showDetail&id_articulo=94336&id_seccion=5037&id_ejemplar=9224&id_revista=331
Romero, N. (2003). Comentarios sobre la definición de autómata celular. Boletín de la Asociación Matemática Venezolana, 10(1), 59-97. Available at: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/BAMV/conten/vol10/neptali.pdf
Saldaña, J. (2010). La modelización de la propagación de epidemias. Matematicalia, 6(2). Retrieved from: http://dugi-doc.udg.edu/bitstream/handle/10256/7482/modelizaci%C3%B3n-propagaci%C3%B3n-epidemias.pdf?sequence=1
The Center for Food Security & Public Health (2009). Influenza-Factsheet. Ames, IO: Iowa State University.
Toole, M. (2000). Enfermedades transmisibles y su control. In Impacto de los desastres en la salud pública (pp. 79-100). Bogotá, Colombia: Organización Panamericana de la Salud.
Torok, M. (2003). Epidemic curves ahead. Focus on Field Epidemiology, 1(5). Retrieved from: http://nciph.sph.unc.edu/focus/vol1/issue5/1-5EpiCurves_issue.pdf
Vázquez, J. & Oliver J. (2008). Evolución de autómatas celulares utilizando algoritmos genéticos. Retrieved from: https://www.cs.us.es/cursos/ia1-2008/trabajos/articulo1.pdf
Wolfram, S. (1984). Universality and complexity in cellular automata. Retrieved from: http://www.stephenwolfram.com/publications/cellular-automata-complexity/
Wolfram. S (1988). Cellular automaton supercomputing. In Cellular automata and complexity: Collected papers by Stephen Wolfram, (pp. 499-509). Reading, MA: Addison-Wesley. Available at: http://www.stephenwolfram.com/publications/cellular-automata-complexity/
Yang, X. & Young, Y. (2005). Cellular automata, PDEs, and pattern formation. In Handbook of bioinspired algorithms and applications, (pp. 271-282). Boca Raton, FL: Taylor and Frnacis. Available at: http://arxiv.org/ftp/arxiv/papers/1003/1003.1983.pdf
Andreasen, V., Viboud, C., & Simonsen, L. (2008). Epidemiologic characterization of the 1918 influenza pandemic summer wave in Copenhagen: implications for pandemic control strategies. Journal of Infectious Diseases, 197(2), 270-278). Available at: http://www.ncbi.nlm.nih.gov/pubmed/18194088
Arenas, A. J., González-Parra, G., & Moraño, J. A. (2009). Stochastic modeling of the transmission of respiratory syncytial virus (RSV) in the region of Valencia, Spain. Biosys, 96(3), 206-212.
Beauchemina, C., Samuelb, J. & Tuszynskia, J. (2005). A simple cellular automaton model for influenza A viral infections. Journal of Theoretical Biology 232, 223-234.
Burniaková, L. (2007). The mathematics of infectious diseases [master thesis]. Comenius University: Bratislava, Eslovaquia. Retrieved from: http://diplomovka.sme.sk/zdroj/3138.pdf
Chowell, G., Ammon, C., Hengartner, N., & Hyman, J. (2006). Transmission dynamics of the great influenza pandemic of 1918 in
Geneva, Switzerland: Assessing the effects of hypothetical interventions. Journal of Theoretical Biology, 241(2), 93-204). Available at: http://math.lanl.gov/~mac/papers/bio/GAHH06b.pdf
Coburn, B., Wagner, B., & Blower, S. (2009) Modeling epidemics and pandemics: Insights into the future of swine flu (H1N1). BMC Medicine, 7. doi:10.1186/1741-7015-7-30 Available at: http://www.biomedcentral.com/content/pdf/1741-7015-7-30.pdf
Cuesta, H., Trueba, A., & Ruiz J. (2012). Autómata Celular Estocástico paralelizado por GPU aplicado a la simulación de enfermedades infecciosas en grandes poblaciones. Acta Universitaria, 22(6), 16-19. Available at: http://www.actauniversitaria.ugto.mx/index.php/acta/article/viewFile/356/pdf
Cunha, B. (2004). Influenza: Historical aspects of epidemics and pandemics. Infectious Disease Clinics of North America, 18(1), 148-155.
Doracelli, H. & Ospina, J. (2007). Bases para la modelación de epidemias: el Caso del síndrome respiratorio agudo severo en Canadá. Revista Salud Pública, 9(1), 121-123.
Dubacq, J.-C., Durand, B., & Formenti, E. (2001). Kolmogorov complexity and cellular automata classification. Theoretical Computer Science, 259(1), 271-285. doi:10.1016/S0304-3975(00)00012-8
Firestone, S., Cogger, N., Ward, M., Toribio, J., Moloney, B., & Dhand, N. (2012). The Influence of meteorology on the spread of influenza: Survival analysis of an equine influenza (A/H3N8) Outbreak. PloS One, 7(4). e35284. doi: 10.1371/journal.pone.0035284
Fonseca, F. & Blanco, W. (2010). Mecánica estadística de redes y propagación de enfermedades infecciosas. Revista Colombiana de Física, 42(3), 322-323. Available at: http://revcolfis.org/ojs/index.php/rcf/article/viewArticle/420316
Ganguly, N., Sikdar, B., Deutsch, A., Canright, G., & Chaudhuri (2003). A survey on cellular automata. Retrieved from: http://www.cs.unibo.it/bison/publications/CAsurvey.pdf
Gharib-Zahedi, R. M. & Ghaemi, M. (2012). Kinetics of hepatitis B virus infection: A cellular automaton model study. Journal of Paramedical Sciences, 3(3). Retrieved from: http://journals.sbmu.ac.ir/jps/article/download/3482/3130
Gómez, G. & Vargas-De-León, C. (2012). Modeling control strategies for influenza A H1N1 epidemics: SIR models. Revista Mexicana de Física, S58(1), 37-43. Available at: http://rmf.fciencias.unam.mx/~raem/caos/SC-7_1.pdf
Hauska, H. & Linde, A. (2008). The Russian influenza in Sweden in 1889-90: An example of geographic information system analysis. Eurosurveillance, 13(49). Retrieved from: http://www.ncbi.nlm.nih.gov/pubmed/19081003
Hoya, S., Martin del Rey, A. & Rodríguez, G. (2009). Using cellular automata to simulate epidemic diseases. Applied Mathematical Sciences, 3(20), 959-968. Available at: http://www.m-hikari.com/ams/ams-password-2009/ams-password17-20-2009/delreyAMS17-20-2009.pdf
Knipl, D. & Rӧst, G. (2011). Influenza models with wolfram mathematica [blog - Interesting mathematical problems in sciences and everyday life - 2011]. Retrieved from: http://www.model.u-szeged.hu/etc/edoc/imp/GRost/GRost.pdf
Lahoz-Beltrá, R. (2004). Bioinformática: simulación, vida artificial e inteligencia artificial. Madrid, España: Díaz de Santos.
Madrigal, J., Muñoz, L.A., & Garcia, M.J. (2011). Autómatas celulares en redes de Boltzmann [paper in VIII Congreso Colombiano de Métodos Numéricos: Simulación en Ciencias y Aplicaciones Industriales 8CCMN – 2011, Agosto. 10-12, 2011, Medellín, Colombia, Universidad EAFIT]. Retrieved from: http://mecanica.eafit.edu.co/8ccmn/articulos/Madrigal-8ccmn2011.pdf
Martin, O., Odlyzko, A., Wolfram, S. (1984). Algebraic properties of cellular automata. Communications in mathematical physics, 93(2), 219-258. Available at: http://www.stephenwolfram.com/publications/academic/algebraic-properties-cellular-automata.pdf
Martin-del-Rey, A. (2009). Epidemiologia matemática usando autómatas celulares sobre grafos. In XXI Congreso de Ecuaciones Diferenciales y Aplicaciones / XI Congreso de Matemática Aplicada [Actas del Cyda]. Retrieved from: http://matematicas.uclm.es/cedya09/archive/textos/35_Martin-del-Rey-A.pdf
Mendes-dos-Santos, L. & Silva-de.Souza, F. (2012). Uma análise do modelo SIR aplicado ao estudo da influenza A. In CEMAC Nordeste 2012, (pp.20-23). Retrieved from: http://www.sbmac.org.br/cmacs/cmac-ne/2012/trabalhos/PDF/113.pdf
Mitchell, M., Hraber, P. & Crutchfield, J. (1993). Revisiting the edge of chaos: Evolving cellular automata to perform computations [Report No. SFI Working Paper 93-03-014]. Retrieved from: http://arxiv.org/pdf/adap-org/9303003.pdf
Morse, S. (1995). Factors in the emergence of infectious diseases. Emerging Infectious Diseases, 1(1), 7-15. Available at http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2626828/pdf/8903148.pdf
Ramasco, J. (2012). Predicción de los patrones de propagación de contacto con ordenadores. Medicina Balear, 28(1), 41-47. Available at: http://www.imbiomed.com.mx/1/1/articulos.php?method=showDetail&id_articulo=94336&id_seccion=5037&id_ejemplar=9224&id_revista=331
Romero, N. (2003). Comentarios sobre la definición de autómata celular. Boletín de la Asociación Matemática Venezolana, 10(1), 59-97. Available at: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/BAMV/conten/vol10/neptali.pdf
Saldaña, J. (2010). La modelización de la propagación de epidemias. Matematicalia, 6(2). Retrieved from: http://dugi-doc.udg.edu/bitstream/handle/10256/7482/modelizaci%C3%B3n-propagaci%C3%B3n-epidemias.pdf?sequence=1
The Center for Food Security & Public Health (2009). Influenza-Factsheet. Ames, IO: Iowa State University.
Toole, M. (2000). Enfermedades transmisibles y su control. In Impacto de los desastres en la salud pública (pp. 79-100). Bogotá, Colombia: Organización Panamericana de la Salud.
Torok, M. (2003). Epidemic curves ahead. Focus on Field Epidemiology, 1(5). Retrieved from: http://nciph.sph.unc.edu/focus/vol1/issue5/1-5EpiCurves_issue.pdf
Vázquez, J. & Oliver J. (2008). Evolución de autómatas celulares utilizando algoritmos genéticos. Retrieved from: https://www.cs.us.es/cursos/ia1-2008/trabajos/articulo1.pdf
Wolfram, S. (1984). Universality and complexity in cellular automata. Retrieved from: http://www.stephenwolfram.com/publications/cellular-automata-complexity/
Wolfram. S (1988). Cellular automaton supercomputing. In Cellular automata and complexity: Collected papers by Stephen Wolfram, (pp. 499-509). Reading, MA: Addison-Wesley. Available at: http://www.stephenwolfram.com/publications/cellular-automata-complexity/
Yang, X. & Young, Y. (2005). Cellular automata, PDEs, and pattern formation. In Handbook of bioinspired algorithms and applications, (pp. 271-282). Boca Raton, FL: Taylor and Frnacis. Available at: http://arxiv.org/ftp/arxiv/papers/1003/1003.1983.pdf
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2015-12-03
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