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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 137854, 10 pages
http://dx.doi.org/10.1155/2009/137854
Research Article

The Effect of Spatial Scale on Predicting Time Series: A Study on Epidemiological System Identification

1Pós-graduação em Engenharia Elétrica, Escola de Engenharia, Universidade Presbiteriana Mackenzie, Rua da Consolação, n.896, 01302-907 São Paulo, SP, Brazil
2Departamento de Engenharia de Telecomunicações e Controle, Escola Politécnica, Universidade de São Paulo, Avendia Professor Luciano Gualberto, travessa 3, n.380, 05508-900 São Paulo, SP, Brazil
3Departamento de Fisiologia, Instituto de Biociências, Universidade de São Paulo, Rua do Matão, travessa 14, n.321, 05508-900 São Paulo, SP, Brazil

Received 28 October 2008; Revised 2 February 2009; Accepted 23 February 2009

Academic Editor: Elbert E. Neher Macau

Copyright © 2009 L. H. A. Monteiro et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Ljung, System Identification: Theory for the User, Prentice-Hall, Upper Saddle River, NJ, USA, 1999.
  2. W. A. Calder, III, “Scaling of physiological processes in homeothermic animals,” Annual Review of Physiology, vol. 43, pp. 301–322, 1981. View at Publisher · View at Google Scholar · View at PubMed
  3. A. Bejan, Shape and Structure: From Engineering to Nature, Cambridge University Press, Cambridge, UK, 2000. View at Zentralblatt MATH
  4. G. I. Barenblatt, Scaling, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, UK, 2003. View at Zentralblatt MATH · View at MathSciNet
  5. A. Alexandrou, Principles of Fluid Mechanics, Prentice-Hall, Upper Saddle River, NJ, USA, 2001.
  6. Arizona Department of Health Services, Reported Cases of Notifiable Diseases by Year (1994–2004), October 2008, http://www.azdhs.gov/phs/oids/stats/pdf/t3_cases1994-2004.pdf.
  7. L. H. A. Monteiro, H. D. B. Chimara, and J. G. Chaui-Berlinck, “Big cities: shelters for contagious diseases,” Ecological Modelling, vol. 197, no. 1-2, pp. 258–262, 2006. View at Publisher · View at Google Scholar
  8. L. H. A. Monteiro, J. B. Sasso, and J. G. Chaui-Berlinck, “Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time,” Ecological Modelling, vol. 201, no. 3-4, pp. 553–557, 2007. View at Publisher · View at Google Scholar
  9. P. H. T. Schimit and L. H. A. Monteiro, “On the basic reproduction number and the topological properties of the contact network: an epidemiological study in mainly locally connected cellular automata,” Ecological Modelling, vol. 220, no. 7, pp. 1034–1042, 2009. View at Publisher · View at Google Scholar
  10. J. D. Murray, Mathematical Biology. I. An Introduction, vol. 17 of Interdisciplinary Applied Mathematics, Springer, New York, NY, USA, 3rd edition, 2002. View at Zentralblatt MATH · View at MathSciNet
  11. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, “Complex networks: structure and dynamics,” Physics Reports, vol. 424, no. 4-5, pp. 175–308, 2006. View at Google Scholar · View at MathSciNet
  12. J. R. C. Piqueira, M. Q. Oliveira, and L. H. A. Monteiro, “Synchronous state in a fully connected phase-locked loop network,” Mathematical Problems in Engineering, vol. 2006, Article ID 52356, 12 pages, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  13. S. Yakowitz, J. Gani, and R. Hayes, “Cellular automaton modeling of epidemics,” Applied Mathematics and Computation, vol. 40, no. 1, pp. 41–54, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. A. Fuentes and M. N. Kuperman, “Cellular automata and epidemiological models with spatial dependence,” Physica A, vol. 267, no. 3, pp. 471–486, 1999. View at Publisher · View at Google Scholar
  15. M. Mitchell, P. T. Hraber, and J. P. Crutchfield, “Revisiting the edge of chaos: evolving cellular automata to perform computations,” Complex Systems, vol. 7, no. 2, pp. 89–130, 1993. View at Google Scholar · View at Zentralblatt MATH
  16. S. A. Billings and Y. Yang, “Identification of probabilistic cellular automata,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 33, no. 2, pp. 225–236, 2003. View at Publisher · View at Google Scholar · View at PubMed
  17. N. Ganguly, P. Maji, B. K. Sikdar, and P. P. Chaudhuri, “Design and characterization of cellular automata based associative memory for pattern recognition,” IEEE Transactions on Systems, Man, and Cybernetics, Part B, vol. 34, no. 1, pp. 672–679, 2004. View at Publisher · View at Google Scholar
  18. P. P. B. de Oliveira, J. C. Bortot, and G. M. B. Oliveira, “The best currently known class of dynamically equivalent cellular automata rules for density classification,” Neurocomputing, vol. 70, no. 1–3, pp. 35–43, 2006. View at Publisher · View at Google Scholar
  19. S. Suzuki and T. Saito, “Synthesis of desired binary cellular automata through the genetic algorithm,” in Proceedings of the 13th International Conference on Neural Information Processing (ICONIP '06), vol. 4234 of Lecture Notes in Computer Science, pp. 738–745, Hong Kong, October 2006. View at Publisher · View at Google Scholar
  20. Central Intelligence Agency, The 2008 World Factbook, U.S. Government Printing Office, Washington, DC, USA, 2008.
  21. H. Rawson, A. Crampin, and N. Noah, “Deaths from chickenpox in England and Wales 1995–7: analysis of routine mortality data,” British Medical Journal, vol. 323, no. 7321, pp. 1091–1093, 2001. View at Publisher · View at Google Scholar
  22. E. Holmes, “Basic epidemiological concepts in a spatial context,” in Spatial Ecology, D. Tilman and P. Kareiva, Eds., pp. 111–136, Princeton University Press, Princeton, NJ, USA, 1997. View at Google Scholar
  23. M. G. Turner, R. V. O'Neill, R. H. Gardner, and B. T. Milne, “Effects of changing spatial scale on the analysis of landscape pattern,” Landscape Ecology, vol. 3, no. 3-4, pp. 153–162, 1989. View at Publisher · View at Google Scholar
  24. J. L. Dungan, J. N. Perry, M. R. T. Dale et al., “A balanced view of scale in spatial statistical analysis,” Ecography, vol. 25, no. 5, pp. 626–640, 2002. View at Publisher · View at Google Scholar
  25. D. L. DeAngelis and J. H. Petersen, “Importance of the predator's ecological neighborhood in modeling predation on migrating prey,” Oikos, vol. 94, no. 2, pp. 315–325, 2001. View at Publisher · View at Google Scholar
  26. M. Pascual, P. Mazzega, and S. A. Levin, “Oscillatory dynamics and spatial scale: the role of noise and unresolved pattern,” Ecology, vol. 82, no. 8, pp. 2357–2369, 2001. View at Google Scholar