Mathematical Model for Dengue Virus Infected Populations with Fuzzy Differential Equations

  • A. RajkumarEmail author
  • C. JesurajEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 955)


The behaviors of Dengue Virus Infected Population model in Fuzzy and Interval Environment are discussed here. Modeling the environments in fuzzy differential equation and used to solve in different environments to get accurate solution by triangular fuzzy numbers. To identify these two different environments, how the behaviors of model can changes, finally we discussed briefly with two examples in each environment.


Dengue virus FDE (fuzzy differential equation) Fuzzy number 


  1. 1.
    Chang, S.S., Zadeh, L.A.: On fuzzy mapping and control. IEEE Trans. Syst. Man Cybern. 2, 330–340 (1972)MathSciNetGoogle Scholar
  2. 2.
    Bede, B., Ruda, I.J., Bencsik, A.L.: First order linear fuzzy differential equations under generalized differentiability. Inf. Sci. 177, 1648–1662 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Akın, O., Oruc, O.: A Prey predator model with fuzzy initial values. Hacettepe J. Math. Stat. 41(3), 387–395 (2012)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Mondal, S.P., Roy, T.K.: First order linear homogeneous fuzzy ordinary differential equation based on lagrange multiplier method. J. Soft Comput. Appl. 2013, 1–17 (2013)Google Scholar
  5. 5.
    Mahata, A., Roy, B., Mondal, S.P., Alam, S.: Application of ordinary differential equation in glucose-insulin regulatory system modeling in fuzzy environment. Ecol. Genet. Genom. 3, 60–66 (2017)Google Scholar
  6. 6.
    Sharma, S., Samanta, G.P.: Optimal harvesting of a two species competition model with imprecise biological parameters. Nonlinear Dyn. 77, 1101–1119 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Pandit, P., Singh, P.: Prey predator model with fuzzy initial conditions. Int. J. Eng. Innov. Technol. (IJEIT) 3(12) (2014)Google Scholar
  8. 8.
    Pal, D., Mahapatra, G.S.: A bioeconomic modeling of two-prey and one-predator fishery model with optimal harvesting policy through hybridization approach. Appl. Math. Comput. 242, 748–763 (2014)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Mondal, S.P., Roy, T.K.: System of differential equation with initial value as triangular intuitionistic fuzzy number and its application. Int. J. Appl. Comput. Math. 3, 449–474 (2015)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Paul, S., Mondal, S.P., Bhattacharya, P.: Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach. Model. Earth Syst. Environ. 2, 70 (2016)CrossRefGoogle Scholar
  11. 11.
    Mahata, A., Mondal, S.P., Alam, S., Roy, B.: Mathematical model of glucose-insulin regulatory system on diabetes mellitus in fuzzy and crisp environment. Ecol. Genet. Genom. 2, 25–34 (2017)Google Scholar
  12. 12.
    Hussain, S.A.I., Mondal, S.P., Mandal, U.K.: A holistic-based multi-criterion decision-making approach for solving engineering sciences problem under imprecise environment. In: Handbook of Research on Modeling, Analysis, and Application of Nature (2018)Google Scholar
  13. 13.
    Kaleva, O.: Fuzzy differential equation. Fuzzy Sets Syst. 24, 301–317 (1987)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kaleva, O.: The Cauchy problems for fuzzy differential equations. Fuzzy Sets Syst. 35, 389–396 (1990)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Buckley, J.J., Feuring, T., Hayashi, Y.: Linear systems of first order ordinary differential equations: fuzzy initial conditions. Soft Comput. 6, 415–421 (2001)CrossRefGoogle Scholar
  16. 16.
    Felix, A., Christopher, S., Devadoss, A.V.: A nonagonal fuzzy numbers and its arithmetic operation. IJMAA 2, 185–195 (2015)Google Scholar
  17. 17.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets. Physica-Verlag, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Kharal, A.: Homeopathic drug selection using intuitionistic fuzzy sets. Homeopathy 98(1), 35–39 (2009)CrossRefGoogle Scholar
  19. 19.
    Rajkumar, A., Jesuraj, C.: A new approach to solve fuzzy differential equation using intuitionistic nanaogonal fuzzy numbers. In: Proceedings of Second International Conference on FEAST 2018, pp. 187–194 (2018)Google Scholar
  20. 20.
    Buckley, J.J., Feuring, T.: Fuzzy differential equations. Fuzzy Sets Syst. 110, 43–54 (2000)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Hindustan Institute of Technology and ScienceChennaiIndia
  2. 2.IFET Colleges of EngineeringVillupuramIndia

Personalised recommendations