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The stochastic evolution of rumors within a population

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  • Dauhoo, Muhammad Zaid
  • Juggurnath, Diksha
  • Badurally Adam, Noure-Roukayya

Abstract

We study rumor propagation process with incubation and constant immigration. We take into account a deterministic rumor spreading model and demonstrate the persistence of a rumor when the basic reproduction number is greater than one. Due to the presence of a randomness in the influence that the incubators exert on ignorants, we extrapolate the deterministic rumor model to a stochastic one by using a stochastic coefficient for the term representing the latter influence within the system. The existence and boundedness of both local and global solutions are demonstrated. We prove the uniqueness of these solutions. Conditions of extinction is also established. We perform numerical simulations to verify our stochastic model. The present work can assist decision takers in the analysis of the dynamical evolution of rumors in a given society as well as in the study of information dissemination strategies.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:matsoc:v:82:y:2016:i:c:p:85-96
    DOI: 10.1016/j.mathsocsci.2016.05.002
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Cheng, Yingying & Huo, Liang’an & Zhao, Laijun, 2020. "Rumor spreading in complex networks under stochastic node activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    2. Huang, Jia-Ping & Koster, Maurice & Lindner, Ines, 2016. "Diffusion of behavior in network games with threshold dynamics," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 109-118.

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