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Dengue Model Described by Differential Inclusions

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Advances in Computational Intelligence (IWANN 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6692))

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Abstract

In this paper we formulate a differential inclusion to model an epidemic outbreak of Dengue fever in the Cuban conditions. The model takes into account interaction of human and mosquito populations as well as vertical transmission in the mosquito population. Finally, we propose a mathematical framework allowing us to make suitable predictions about the populations of humans, mosquitoes and eggs infected during the epidemic time.

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References

  1. Aubin, J.-P., Cellina, A.: Differential Inclusions, Set-Valued Maps and Viability Theory. Springer, Heidelberg (1984)

    Book  MATH  Google Scholar 

  2. Barrios, J., Piétrus, A., Marrero, A., De Arazoza, H.: Hiv model described by differential inclusions. In: Cabestany, J., Sandoval, F., Prieto, A., Corchado, J.M. (eds.) IWANN 2009. LNCS, vol. 5517, pp. 909–916. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Briegel, H., Kaiser, C.: Life-span of mosquitoes (culicidae, diptera) under laboratory conditions. Gerontologia 19, 240–249 (1973)

    Article  Google Scholar 

  4. Castaing, C.: Sur les équations différentielles multivoques. C.R. Acad. Sci. Paris 263, 63–66 (1966)

    MathSciNet  MATH  Google Scholar 

  5. Diamond, P.: Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations. IEEE Transactions on Fuzzy Systems 7(6) (December 1999)

    Google Scholar 

  6. Hermes, H.: The generalized differential equation \(\dot{x}\in r(t,x)\). Adv. in Math. 4, 149–169 (1970)

    Article  MATH  Google Scholar 

  7. Ishikawa, H., Ishii, A., et al.: A mathematical model for the transmission of plasmodium vivax malaria. Parasitol. Int. 52, 81–93 (2003)

    Article  Google Scholar 

  8. Keener, G.: Detailed observations on the life history of anopheles quadrimaculatus. J. Natl. Malaria. Soc. 4, 263–270 (1945)

    Google Scholar 

  9. Lempio, F., Veliov, V.: Discrete approximation of differential inclusions. Bayreuther Mathematische Schriften 54, 149–232 (1998)

    MathSciNet  MATH  Google Scholar 

  10. Styer, L.M., Carey, J.R., et al.: Mosquitoes do Senesce: Departure from the Paradigm of Constant Mortality. Am. J. Trop. Med. Hyg. 76(1), 111–117 (2007)

    Google Scholar 

  11. Teck-Cheong, L.: On fixed point stability for set-valued contractive mappings with application to generalized differential equations. Journal of Mathematical Analysis and Applications 110, 436–441 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Veliov, V.: On the time-discretization of control systems. SIAM J. Control Optim. 35(5), 1470–1486 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Université des Antilles et de la Guyane, LAMIA (EA4540), France

    Jorge Barrios & Alain Piétrus

  2. Facultad de Matemática y Computación, Universidad de La Habana, Cuba

    Jorge Barrios, Aymée Marrero & Héctor de Arazoza

  3. Dpto. Tecnología Electrónica, E.T.S. Ing. Telecomunicación, Universidad de Málaga, Spain

    Gonzalo Joya

Authors
  1. Jorge Barrios
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  2. Alain Piétrus
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  3. Aymée Marrero
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  4. Héctor de Arazoza
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  5. Gonzalo Joya
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Editor information

Editors and Affiliations

  1. Departament d’Enginyeria Electrònica, Universitat Politècnica de Catalunya (UPC), Campus Nord, Edificio C4, c/ Gran Capità s/n, 08034, Barcelona, Spain

    Joan Cabestany

  2. Department of Computer Architecture and Computer Technology, University of Granada, C/ Periodista Daniel Saucedo Aranda, 18071, Granada, Spain

    Ignacio Rojas

  3. Departamento Tecnologia Eletrónica, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Gonzalo Joya

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© 2011 Springer-Verlag Berlin Heidelberg

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Barrios, J., Piétrus, A., Marrero, A., de Arazoza, H., Joya, G. (2011). Dengue Model Described by Differential Inclusions. In: Cabestany, J., Rojas, I., Joya, G. (eds) Advances in Computational Intelligence. IWANN 2011. Lecture Notes in Computer Science, vol 6692. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21498-1_68

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  • DOI: https://doi.org/10.1007/978-3-642-21498-1_68

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21497-4

  • Online ISBN: 978-3-642-21498-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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