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Analyzing the Dynamics of a Rumor Transmission Model with Incubation

Author

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  • Liang'an Huo
  • Peiqing Huang
  • Chun-xiang Guo

Abstract

This paper considers a rumor transmission model with incubation that incorporates constant recruitment and has infectious force in the latent period and infected period. By carrying out a global analysis of the model and studying the stability of the rumor-free equilibrium and the rumor-endemic equilibrium, we use the geometric approach for ordinary differential equations which is based on the use of higher-order generalization of Bendixson’s criterion. It shows that either the number of rumor infective individuals tends to zero as time evolves or the rumor persists. We prove that the transcritical bifurcation occurs at crosses the bifurcation threshold by projecting the flow onto the extended center manifold. Since the rumor endemic level at the equilibrium is a continuous function of , as a consequence for successful eradication of the rumor, one should simply reduce continuously below the threshold value 1. Finally, the obtained results are numerically validated and then discussed from both the mathematical and the sociological perspectives.

Suggested Citation

  • Liang'an Huo & Peiqing Huang & Chun-xiang Guo, 2012. "Analyzing the Dynamics of a Rumor Transmission Model with Incubation," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-21, April.
  • Handle: RePEc:hin:jnddns:328151
    DOI: 10.1155/2012/328151
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    Cited by:

    1. Dauhoo, Muhammad Zaid & Juggurnath, Diksha & Badurally Adam, Noure-Roukayya, 2016. "The stochastic evolution of rumors within a population," Mathematical Social Sciences, Elsevier, vol. 82(C), pages 85-96.
    2. Jia, Pingqi & Wang, Chao & Zhang, Gaoyu & Ma, Jianfeng, 2019. "A rumor spreading model based on two propagation channels in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 342-353.
    3. Jianhong Chen & Hongcai Ma & Shan Yang, 2023. "SEIOR Rumor Propagation Model Considering Hesitating Mechanism and Different Rumor-Refuting Ways in Complex Networks," Mathematics, MDPI, vol. 11(2), pages 1-22, January.
    4. Ping Jiang & Xiangbin Yan, 2019. "A quantitative model for the spread of online information," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1981-2001, July.

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