A Spatial Stochastic Model for Rumor Transmission

Coletti, Cristian F.; Rodríguez, Pablo M.; Schinazi, Rinaldo B.

doi:10.1007/s10955-012-0469-y

Cited by 23 publications

(23 citation statements)

References 15 publications

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“…Variations of the Maki-Thompson rumor model were considered in several graphs. For instance, the survival of the rumor was studied in Moreno et al (2004) and Isham et al (2010) when the population is represented by a random or complex network, and in Coletti et al (2012) when the population is represented by the d-dimensional hypercubic lattice.…”

Section: Introductionmentioning

confidence: 99%

Rumor Processes on $$\mathbb {N}$$ N and Discrete Renewal Processes

et al. 2014

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We study two rumor processes on N, the dynamics of which are related to an SI epidemic model with long range transmission. Both models start with one spreader at site 0 and ignorants at all the other sites of N, but differ by the transmission mechanism. In one model, the spreaders transmit the information within a random distance on their right, and in the other the ignorants take the information from a spreader within a random distance on their left.We obtain the probability of survival, information on the distribution of the range of the rumor and limit theorems for the proportion of spreaders. The key step of our proofs is to show that, in each model, the position of the spreaders on N can be related to a suitably chosen discrete renewal process.Date: December 18, 2013.

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Section: Introductionmentioning

confidence: 99%

Rumor Processes on $$\mathbb {N}$$ N and Discrete Renewal Processes

et al. 2014

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“…To illustrate our approach, we return to the spreading process (3). Assuming that μn, σ figure 2, one easily discerns the individual effects from movement and spreading while the effects of spreading can hardly be seen in figure 3.…”

Section: Examplementioning

confidence: 99%

“…Some authors also consider epidemic rumour processes where individuals are localised on a line [5] or a d-dimensional lattice [3]. In this case, rumour spreading depends on the distance to other individuals.…”

Section: Introductionmentioning

confidence: 99%

Spreading rumours in Euclidean space

Fiems

Turck

2013

SIGMETRICS Perform. Eval. Rev.

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This paper considers the process of spreading rumours in Euclidean space. The rumour (or epidemic) process under study includes (i) a discrete-time stochastic arrival process of new spatially distributed rumours and (ii) a stochastic process of linear transformations of the current rumours which allows for modelling mobility as well as dispersion of rumours. Inspired by linear filtering theory, an affine stochastic recursion in characteristic-function space is studied and numerical transform inversion is used to study the distribution of rumours in space.

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“…We refer the reader to [7,12,13,14] for a review of results and generalizations of these models. Also, many modifications of these models have been considered assuming that the population is not necessarily homogeneous nor totally mixing, see [1,3,5,16,17] and the references therein. The results obtained in that direction rely mainly on mean-field approximations, computational simulations, or partial qualitative results.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic behavior for a modified Maki-Thompson model with directed inter-group interactions

Grejo

Rodríguez

2019

Journal of Mathematical Analysis and Applications

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In this work we propose a new extension for the Maki-Thompson rumor model which incorporates inter-group directed contacts. The model is defined on an homogeneously mixing population where the existence of two differentiated groups of individuals is assumed. While individuals of one group have an active role in the spreading process, individuals of the other group only contribute in stifling the rumor provided they would contacted. For this model we measure the impact of dissemination by studying the remaining proportion of ignorants of both groups at the end of the process. In addition we discuss some examples and possible applications.

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A Spatial Stochastic Model for Rumor Transmission

Cited by 23 publications

References 15 publications

Rumor Processes on $$\mathbb {N}$$ N and Discrete Renewal Processes

Rumor Processes on $$\mathbb {N}$$ N and Discrete Renewal Processes

Spreading rumours in Euclidean space

Asymptotic behavior for a modified Maki-Thompson model with directed inter-group interactions

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