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.
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References
Biomat04, http://biomat04.wikispaces.com/conceitos
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)
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)
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)
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)
Godo, L., Sandri, S.: A similarity-based approach to deal with inconsistency in systems of fuzzy gradual rules. In: Proc. IPMU 2002 (2002)
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)
Hethcote, H.W.: The Mathematics of Infectious Diseases. SIAM Review 42(4), 599–653 (2000)
Ierusalimschy, R.: Programming in Lua. 2nd edn. Lua.org (2006)
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)
Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall (1995)
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)
Ministério da Saúde. Guia de vigilância epidemiológica, 6th edn. Ministério da Saüde, Brasília (2005)
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)
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)
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)
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)
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)
Von Neumann, J.: Theory of Self-Reproducing Automata. A.W. Burks (1966)
Wolfram, S.: Theory and Application of Cellular Automata. World Scientific (1986)
Yang, H.M.: Epidemiologia matemática: Estudos dos Efeitos da Vacinac̨ão em Doenc̨as de Transmissão Direta. Ed. da Unicamp (2001)
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da Costa, W., Medeiros, L., Sandri, S. (2013). A Fuzzy Cellular Automata for SIR Compartmental Models. In: Masulli, F., Pasi, G., Yager, R. (eds) Fuzzy Logic and Applications. WILF 2013. Lecture Notes in Computer Science(), vol 8256. Springer, Cham. https://doi.org/10.1007/978-3-319-03200-9_24
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DOI: https://doi.org/10.1007/978-3-319-03200-9_24
Publisher Name: Springer, Cham
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