An SIR rumor pairwise model with spreading age

Volume 14, Issue 3, pp 148--162 http://dx.doi.org/10.22436/jnsa.014.03.04

Publication Date: October 15, 2020 Submission Date: July 05, 2020 Revision Date: August 07, 2020 Accteptance Date: August 17, 2020

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1133 Downloads
• 2089 Views

Authors

Yao Liu - School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, P. R. China. Jinxian Li - School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, P. R. China.

Abstract

In this paper, we extend the classical rumor model with non-Markovian recovery process in a complex network. We follow the ideas from R\"{o}st to analyze the pairwise model; then, the hyperbolic system can be transformed into integro-differential equations. For the rumor model, the reproduction number is obtained. Next, we use numerical simulation to verify the accuracy of the result. In the end, we focus on how the three different distributions of recovery time with spreading age influence on rumor model. The result illustrates the significant effect of different distribution functions on the process of rumor spreading.

Share and Cite

Keywords

• Rumor pairwise model
• spreading age
• reproduction number
• numerical simulation

MSC

•  05C82
•  37N25
•  92D25

References

• [1] G. Chen, ILSCR rumor spreading model to discuss the control of rumor spreading in emergency, Phys. A, 522 (2019), 88--97
  • View Article
  • MathSciNet


• [2] F. Chunlong, S. Huimin, D. Guohui, Research on an Improved SEIR Network Rumor Propagation Model, J. Intell., 3 (2017), 86--91
  • View Article
  • Google Scholar


• [3] D. J. Daley, D. G. Kendall, Stochastic Rumors, J. Inst. Math. Appl., 1 (1965), 42--55
  • View Article


• [4] A. I. E. Hosni, K. Li, S. Ahmad, Analysis of the impact of online social networks addiction on the propagation of rumors, Phys. A, 542 (2020), 11 pages
  • View Article
  • MathSciNet


• [5] L. Huo, Y. Cheng, Dynamical analysis of a IWSR rumor spreading model with considering the self-growth mechanism and indiscernible degree, Phys. A, 536 (2019), 11 pages
  • View Article
  • MathSciNet


• [6] L. Huo, C. Ma, Dynamical analysis of rumor spreading model with impulse vaccination and time delay, Phys. A, 471 (2017), 653--665
  • View Article
  • MathSciNet


• [7] L. Huo, L. Wang, N. Song, Ch. Ma, B. He, Rumor spreading model considering the activity of spreaders in the homogeneous network, Phys. A, 468 (2017), 855--865
  • View Article
  • MathSciNet


• [8] L. Huo, L. Wang, X. Zhao, Stability analysis and optimal control of a rumor spreading model with media report, Phys. A, 517 (2019), 551--562
  • View Article
  • MathSciNet


• [9] W. Jing, Z. Jin, J. Zhang, An SIR pairwise epidemic model with infection age and demography, J. Biol. Dyn., 12 (2018), 486--508
  • View Article
  • MathSciNet


• [10] K. Kawachi, Deterministic models for rumor transmission, Nonlinear Anal. Real World Appl., 9 (2008), 1989--2028
  • View Article
  • MathSciNet


• [11] R. Li, Y. Li, Z. Meng, Y. Song, G. Jiang, Rumor Spreading Model Considering Individual Activity and Refutation Mechanism Simultaneously, IEEE Access, 8 (2020), 63065–63067
  • View Article
  • Google Scholar


• [12] Q. Liu, T. Li, M. Sun, The analysis of an SEIR rumor propagation model on heterogeneous network, Phys. A, 469 (2017), 372--380
  • View Article
  • MathSciNet


• [13] G. Rost, Z. Vizi, I. Z. Kiss, Pairwise approximation for SIR type network epidemics with non-Markovian recovery, Proc. A, 474 (2018), 21 pages
  • View Article
  • MathSciNet


• [14] N. Sherborne, J. C. Miller, K. B. Blyuss, I. Z. Kiss, Mean-field models for non-Markovian epidemics on networks, J. Math. Biol., 76 (2018), 755--778
  • View Article
  • MathSciNet


• [15] E. Volz, SIR dynamics in random networks with heterogeneous connectivity, J. Math. Biol., 56 (2008), 293--310
  • View Article
  • MathSciNet


• [16] R. R. Wilkinson, F. G. Ball, K. J. Sharkey, The relationships between message passing, pairwise, Kermack-McKendrick and stochastic SIR epidemic models, J. Math. Biol., 75 (2017), 1563--1590
  • View Article
  • MathSciNet


• [17] J. Yang, Y. Chen, Effect of infection age on an SIR epidemic model with demography on complex networks, Phys. A, 479 (2017), 527--541
  • View Article
  • MathSciNet


• [18] H. Yao, X. Gao, SE2IR Invest Market Rumor Spreading Model Considering Hesitating Mechansim, J. Syst. Sci. Inform., 7 (2019), 54--69
  • View Article
  • Google Scholar


• [19] Y. Yao, X. Xiao, C. Zhang, C. Dou, S. Xia, Stability analysis of an SDILR model based on rumor recurrence on social media, Phys. A, 535 (2019), 13 pages
  • View Article
  • MathSciNet


• [20] J. Yang, F. Xu, The Computational Approach for the Basic Reproduction Number of Epidemic Models on Complex Networks, IEEE Acess, 7 (2019), 26474--26479
  • View Article
  • Google Scholar


• [21] J. Zhang, D. Li, W. Jing, Z. Jin, H. Zhu, Transmission dynamics of a two-strain pairwise model with infection age, Appl. Math. Model., 71 (2019), 656--672
  • View Article
  • MathSciNet


• [22] Y. Zhang, J. Zhu, Dynamic behavior of an I2S2R rumor propagation model on weighted contract networks, Phys. A,, 536 (2019), 20 pages
  • View Article
  • MathSciNet