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Design and numerical analysis of fuzzy nonstandard computational methods for the solution of rumor based fuzzy epidemic model

Author

Listed:
  • Dayan, Fazal
  • Rafiq, Muhammad
  • Ahmed, Nauman
  • Baleanu, Dumitru
  • Raza, Ali
  • Ahmad, Muhammad Ozair
  • Iqbal, Muhammad

Abstract

This model extends the classical epidemic model for cyber consumerism by introducing fuzziness to the model. Fuzziness arises due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of confused, escapers and recovered consumers are uncertain due to the different degrees of confusion, escaping and recovery among the individuals of the cyber consumers. The differences can arise, when the cyber consumers under the consideration having distinct habits, customs and different age groups have different degrees of resistance, etc. The chance of transmission of rumors and recovery rates are considered as fuzzy numbers. A rumor-free and two rumor existing-endemic equilibrium points have been derived for the studied model. The model is then solved numerically with fuzzy forward Euler and fuzzy nonstandard finite difference (FNSFD) methods respectively. The numerical and simulation results show that the proposed FNSFD technique is an efficient and reliable tool to deal with such type of dynamical system.

Suggested Citation

  • Dayan, Fazal & Rafiq, Muhammad & Ahmed, Nauman & Baleanu, Dumitru & Raza, Ali & Ahmad, Muhammad Ozair & Iqbal, Muhammad, 2022. "Design and numerical analysis of fuzzy nonstandard computational methods for the solution of rumor based fuzzy epidemic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    • Handle: RePEc:eee:phsmap:v:600:y:2022:i:c:s037843712200379x
    DOI: 10.1016/j.physa.2022.127542
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    1. Nickie Lefevr & Andreas Kanavos & Vassilis C. Gerogiannis & Lazaros Iliadis & Panagiotis Pintelas, 2021. "Employing Fuzzy Logic to Analyze the Structure of Complex Biological and Epidemic Spreading Models," Mathematics, MDPI, vol. 9(9), pages 1-23, April.
    2. Zhao, Laijun & Wang, Xiaoli & Qiu, Xiaoyan & Wang, Jiajia, 2013. "A model for the spread of rumors in Barrat–Barthelemy–Vespignani (BBV) networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5542-5551.
    3. Zhang, Zi-li & Zhang, Zi-qiong, 2009. "An interplay model for rumour spreading and emergency development," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4159-4166.
    4. Wang, Jiajia & Zhao, Laijun & Huang, Rongbing, 2014. "2SI2R rumor spreading model in homogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 153-161.
    5. Keshri, Ajit Kumar & Mishra, Bimal Kumar & Rukhaiyar, Bansidhar Prasad, 2020. "When rumors create chaos in e-commerce," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    6. Zhao, Laijun & Cui, Hongxin & Qiu, Xiaoyan & Wang, Xiaoli & Wang, Jiajia, 2013. "SIR rumor spreading model in the new media age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 995-1003.
    7. Zhao, Laijun & Wang, Qin & Cheng, Jingjing & Chen, Yucheng & Wang, Jiajia & Huang, Wei, 2011. "Rumor spreading model with consideration of forgetting mechanism: A case of online blogging LiveJournal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(13), pages 2619-2625.
    8. Zhao, Laijun & Qiu, Xiaoyan & Wang, Xiaoli & Wang, Jiajia, 2013. "Rumor spreading model considering forgetting and remembering mechanisms in inhomogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 987-994.
    9. Roumen Anguelov & Yves Dumont & Jean Lubuma & Eunice Mureithi, 2013. "Stability Analysis and Dynamics Preserving Nonstandard Finite Difference Schemes for a Malaria Model," Mathematical Population Studies, Taylor & Francis Journals, vol. 20(2), pages 101-122, June.
    10. Laijun Zhao & Xiaoli Wang & Jiajia Wang & Xiaoyan Qiu & Wanlin Xie, 2014. "Rumor-Propagation Model with Consideration of Refutation Mechanism in Homogeneous Social Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-11, August.
    11. Nekovee, M. & Moreno, Y. & Bianconi, G. & Marsili, M., 2007. "Theory of rumour spreading in complex social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 457-470.
    12. Wang, Jiajia & Zhao, Laijun & Huang, Rongbing, 2014. "SIRaRu rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 43-55.
    13. Isham, Valerie & Harden, Simon & Nekovee, Maziar, 2010. "Stochastic epidemics and rumours on finite random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 561-576.
    14. Zhao, Laijun & Wang, Jiajia & Chen, Yucheng & Wang, Qin & Cheng, Jingjing & Cui, Hongxin, 2012. "SIHR rumor spreading model in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2444-2453.
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