Dynamical Behaviors of Fuzzy SIR Epidemic Model

  • Renu VermaEmail author
  • S. P. Tiwari
  • Ranjit Kumar Upadhyay
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 643)


In this paper, we propose and analyze a fuzzy SIR model with an asymptotic transmission rate. Specifically, the fuzziness is due to the consideration of the disease transmission rate, additional death due to disease and rate of recovery from infection as fuzzy sets. Further, a comparative study of the equilibrium points of the disease for the classical and fuzzy models are performed. We study the fuzzy basic reproduction number for groups of infected individuals with different virus loads and compare with a basic reproduction number for the classical model. Finally, a program based on the basic reproduction value \(\mathcal {R}^{f}_{0}\) of disease control is suggested and the numerical simulations are carried out to illustrate the analytical results.


SIR model Fuzzy expected value Fuzzy basic reproduction number Stability 


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Renu Verma
    • 1
    Email author
  • S. P. Tiwari
    • 1
  • Ranjit Kumar Upadhyay
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of Technology (ISM)DhanbadIndia

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