Cellular Automata: control improvements and immunity in the simulation of propagative phenomena
DOI:
https://doi.org/10.18046/syt.v13i35.2149Keywords:
Cellular automata, propagative epidemics, SIR curve model of influenza.Abstract
Two-dimensional cellular automata are a powerful tool for the simulation of complex discrete systems. They are useful in the treatment of propagative phenomena such as epidemics or fires. This paper proposes a series of theoretical, functional, and applicable improvements to the study published in 2009 by Hoya, Martin del Rio, and Rodríguez; it is specifically aimed at controlling the spread patterns in cellular automata with homogeneous resizable lattices, allowing the simulation of immune cell assemblies that act as barriers in the environments studied. As retardant agent, the Susceptible-Infected-Recovered [SIR] epidemiological model of influenza type A was used. The work was developed using MATLAB®, resulting in a collection of more realistic and versatile simulations that seems to fi, in a more accurate way, the observations made on known patterns of influenza.References
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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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