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A Fuzzy Cellular Automata for SIR Compartmental Models

  • Walley da Costa
  • Líliam Medeiros
  • Sandra Sandri
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8256)

Abstract

We propose a representation of the dynamics of epidemics through a compartmental SIR (Susceptible - Infected - Recovered) model, with the combined use of geo-referenced cellular automata and fuzzy systems. In this model, each cell does not correspond to an individual, but to groups of individuals inhabiting the physical space corresponding to the cell. The temporal evolution of the transmission consider is modeled by changes in the size of groups of individuals in each category (susceptible, infected and recovered). We applied our model on the spread of dengue in a region in Southeast Brazil. The application shows that the proposed model, using only a small set of simple fuzzy rules, is able to represent qualitatively the behavior of an epidemiological SIR mode, a rather complex problem.

Keywords

SIR Infectious Diseases Cellular Automata Fuzzy Systems Dengue 

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References

  1. 1.
  2. 2.
    Câmara, G., Cartaxo, R., De Souza, M., Pedrosa, B.M., Vinhas, L., Monteiro, A.M.V., Paiva, J.A., De Carvalho, M.T., Gattass, M.: TerraLib: Technology in Support of GIS Innovation. In: II Brazilian Symposium on Geoinformatics, GeoInfo 2000, São Paulo (2000)Google Scholar
  3. 3.
    Carneiro, T.G.S.: Nested-CA: A Foundation for Multiscale Modeling of Land Use and Land Change. PhD Thesis. INPE, São José dos Campos, Brazil (2006)Google Scholar
  4. 4.
    da Costa, W., Medeiros, L., Sandri, S.: Um estudo de autômatos celulares com sistemas difusos para modelos compartimentais do tipo SIR. In: Proc. II CBSF, Natal, Brazil (2012)Google Scholar
  5. 5.
    Emmendorfer, L.R., Rodrigues, L.A.D.: Um modelo de Autômatos Celulares para o Espalhamento Geográfico de Epidemias. Tendências em Matemática Aplicada e Computacional 2(1), 73–80 (2001)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Godo, L., Sandri, S.: A similarity-based approach to deal with inconsistency in systems of fuzzy gradual rules. In: Proc. IPMU 2002 (2002)Google Scholar
  7. 7.
    Gubler, D.J., Reiter, P., Ebi, K.L., Yap, W., Nasci, R., et al.: Climate variability and change in the United States: potential impacts on vector and rodent-born diseases. Environmental Health Perspectives 109(2), 223–233 (2001)CrossRefGoogle Scholar
  8. 8.
    Hethcote, H.W.: The Mathematics of Infectious Diseases. SIAM Review 42(4), 599–653 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ierusalimschy, R.: Programming in Lua. 2nd edn. Lua.org (2006)Google Scholar
  10. 10.
    Kermack, W., Mckendrick, A.: A Contribution to the Mathematical Theory of Epidemics. Proc. of the Royal Society of London Series A: Mathematical and Physical Sciences 115, 700–721 (1927)CrossRefzbMATHGoogle Scholar
  11. 11.
    Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall (1995)Google Scholar
  12. 12.
    Medeiros, L.C.C., Castilho, C.A.R., Braga, C., de Souza, W.V., Regis, L., Monteiro, A.M.V.: Modeling the dynamic transmission of dengue fever: investigating disease persistence. PLOS Neglected Tropical Diseases 5(1) (2011)Google Scholar
  13. 13.
    Ministério da Saúde. Guia de vigilância epidemiológica, 6th edn. Ministério da Saüde, Brasília (2005)Google Scholar
  14. 14.
    Missio, M.: Um Estudo de Autômatos Celulares com Parâmetros Fuzzy para a Disperão da Febre Aftosa em Bovinos no Mato Grosso do Sul. Biomatemática 16, 31–42 (2006)Google Scholar
  15. 15.
    Oliveira, E., Lacerda, M.J., Barbosa, A.M., Nepomuceno, E.G.: Desenvolvimento de estratégia de controle epidemiológico: Análise espacial e vacinac̨ão a partir do foco da doença. In: Proc XVII CBA, Juiz de Fora, Brazil, pp. 1–6 (2008)Google Scholar
  16. 16.
    Passos, M.N.P., Santos, L.M.J.G., Pereira, M.R.R., Casali, C.G., Fortes, B.P.M.D., Valencia, L.I.O., Alexandre, A.J., Medronho, R.A.: Diferenc̨as clínicas observadas em pacientes com dengue causadas por diferentes sorotipos na epidemia de 2001/2002, ocorrida no município do Rio de Janeiro. Rev. Soc. Bras. Med. Trop. 37(4) (2004)Google Scholar
  17. 17.
    Peixoto, M.S., Barros, L.C.: Um Estudo de Autômatos Celulares para o Espalhamento Geográfico de Epidemias com Parâmetro Fuzzy. TEMA. Tendências em Matemática Aplicada e Computacional, São Paulo 5, 125–133 (2004)Google Scholar
  18. 18.
    Regis, L., Monteiro, A.M., Melo Santos, M.A.V., Silveira, J.C., Furtado, A.F.: Developing new approaches for detecting and preventing Aedes aegypti population outbreaks: basis for surveillance, alert and control system. Mem. I. Oswaldo Cruz 103(1), 50–59 (2008)CrossRefGoogle Scholar
  19. 19.
    Von Neumann, J.: Theory of Self-Reproducing Automata. A.W. Burks (1966)Google Scholar
  20. 20.
    Wolfram, S.: Theory and Application of Cellular Automata. World Scientific (1986)Google Scholar
  21. 21.
    Yang, H.M.: Epidemiologia matemática: Estudos dos Efeitos da Vacinac̨ão em Doenc̨as de Transmissão Direta. Ed. da Unicamp (2001)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Walley da Costa
    • 1
  • Líliam Medeiros
    • 2
  • Sandra Sandri
    • 1
  1. 1.Instituto Nacional de Pesquisas Espaciais - INPESão José dos CamposBrazil
  2. 2.Universidade Estadual Paulista - UnespSão José dos CamposBrazil

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