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A Spatial Stochastic Model for Rumor Transmission

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Abstract

We consider an interacting particle system representing the spread of a rumor by agents on the d-dimensional integer lattice. Each agent may be in any of the three states belonging to the set {0,1,2}. Here 0 stands for ignorants, 1 for spreaders and 2 for stiflers. A spreader tells the rumor to any of its (nearest) ignorant neighbors at rate λ. At rate α a spreader becomes a stifler due to the action of other (nearest neighbor) spreaders. Finally, spreaders and stiflers forget the rumor at rate one. We study sufficient conditions under which the rumor either becomes extinct or survives with positive probability.

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Acknowledgements

C.F.C. was partially supported by FAPESP (grant number 09/52379-8); P.M.R. was supported by FAPESP (grant number 10/06967-2).

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Authors and Affiliations

  1. Centro de Matemática, Computação e Cognição, UFABC, Avenida dos Estados, 5001, Bangu, Santo André, SP, Brazil

    Cristian F. Coletti

  2. Instituto de Ciências Matemáticas e de Computação, USP, Av. Trabalhador São-Carlense 400, Centro, CEP 13560-970, São Carlos, SP, Brazil

    Pablo M. Rodríguez

  3. Department of Mathematics, University of Colorado at Colorado Springs, Colorado Springs, CO, 80933, USA

    Rinaldo B. Schinazi

Authors
  1. Cristian F. Coletti
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  2. Pablo M. Rodríguez
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  3. Rinaldo B. Schinazi
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Correspondence to Pablo M. Rodríguez.

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Coletti, C.F., Rodríguez, P.M. & Schinazi, R.B. A Spatial Stochastic Model for Rumor Transmission. J Stat Phys 147, 375–381 (2012). https://doi.org/10.1007/s10955-012-0469-y

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  • DOI: https://doi.org/10.1007/s10955-012-0469-y

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