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On the classical Maki–Thompson rumour model in continuous time

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  • Selma Belen
  • Erik Kropat
  • Gerhard-Wilhelm Weber

Abstract

In this paper, the Maki–Thompson model is slightly refined in continuous time, and a new general solution is obtained for each dynamics of spreading of a rumour. It is derived an equation for the size of a stochastic rumour process in terms of transitions. We give new lower and upper bounds for the proportion of total ignorants who never learned a rumour and the proportion of total stiflers who either forget the rumour or cease to spread the rumour when the rumour process stops, under general initial conditions. Simulation results are presented for the analytical solutions. The model and these numerical results are capable to explain the behaviour of the dynamics of any other dynamical system having interactions similar to the ones in the stochastic rumour process and requiring numerical interpretations to understand the real phenomena better. The numerical process in the differential equations of the model is investigated by using error-estimates. The estimated error is calculated by the Runge–Kutta method and found either negligible or zero for a relatively small size of the population. This pioneering paper introduces a new mathematical method into Operations research, motivated by various areas of scientific, social and daily life, it presents numerical computations, discusses structural frontiers and invites the interested readers to future research. Copyright Springer-Verlag 2011

Suggested Citation

  • Selma Belen & Erik Kropat & Gerhard-Wilhelm Weber, 2011. "On the classical Maki–Thompson rumour model in continuous time," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(1), pages 1-17, March.
    • Handle: RePEc:spr:cejnor:v:19:y:2011:i:1:p:1-17
    DOI: 10.1007/s10100-009-0120-4
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    References listed on IDEAS

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    1. Watson, Ray, 1987. "On the size of a rumour," Stochastic Processes and their Applications, Elsevier, vol. 27, pages 141-149.
    2. DiFonzo, Nicholas & Bordia, Prashant, 1997. "Rumor and Prediction: Making Sense (but Losing Dollars) in the Stock Market," Organizational Behavior and Human Decision Processes, Elsevier, vol. 71(3), pages 329-353, September.
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    Cited by:

    1. Burcu Gürbüz & Herman Mawengkang & Ismail Husein & Gerhard-Wilhelm Weber, 2022. "Rumour propagation: an operational research approach by computational and information theory," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(1), pages 345-365, March.
    2. Tian, Yong & Ding, Xuejun, 2019. "Rumor spreading model with considering debunking behavior in emergencies," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    3. Chen, Guanghua, 2019. "ILSCR rumor spreading model to discuss the control of rumor spreading in emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 88-97.
    4. Josefa Mula & Marija Bogataj, 2021. "OR in the industrial engineering of Industry 4.0: experiences from the Iberian Peninsula mirrored in CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(4), pages 1163-1184, December.

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