1,348 research outputs found
On the behaviour of a rumour process with random stifling
We propose a realistic generalization of the Maki-Thompson rumour model by
assuming that each spreader ceases to propagate the rumour right after being
involved in a random number of stifling experiences. We consider the process
with a general initial configuration and establish the asymptotic behaviour
(and its fluctuation) of the ultimate proportion of ignorants as the population
size grows to . Our approach leads to explicit formulas so that the
limiting proportion of ignorants and its variance can be computed.Comment: 12 pages, to appear in Environmental Modelling & Softwar
Limit theorems for a general stochastic rumour model
We study a general stochastic rumour model in which an ignorant individual
has a certain probability of becoming a stifler immediately upon hearing the
rumour. We refer to this special kind of stifler as an uninterested individual.
Our model also includes distinct rates for meetings between two spreaders in
which both become stiflers or only one does, so that particular cases are the
classical Daley-Kendall and Maki-Thompson models. We prove a Law of Large
Numbers and a Central Limit Theorem for the proportions of those who ultimately
remain ignorant and those who have heard the rumour but become uninterested in
it.Comment: 13 pages, to appear in SIAM Journal on Applied Mathematic
A large deviations principle for the Maki-Thompson rumour model
We consider the stochastic model for the propagation of a rumour within a
population which was formulated by Maki and Thompson. Sudbury established that,
as the population size tends to infinity, the proportion of the population
never hearing the rumour converges in probability to . Watson later
derived the asymptotic normality of a suitably scaled version of this
proportion. We prove a corresponding large deviations principle, with an
explicit formula for the rate function.Comment: 18 pages, 2 figure
A spatial stochastic model for rumor transmission
We consider an interacting particle system representing the spread of a rumor
by agents on the -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 \lambda. At rate \alpha 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
Phase transition for the Maki-Thompson rumour model on a small-world network
We consider the Maki-Thompson model for the stochastic propagation of a
rumour within a population. We extend the original hypothesis of homogenously
mixed population by allowing for a small-world network embedding the model.
This structure is realized starting from a -regular ring and by inserting,
in the average, additional links in such a way that and are
tuneable parameter for the population architecture. We prove that this system
exhibits a transition between regimes of localization (where the final number
of stiflers is at most logarithmic in the population size) and propagation
(where the final number of stiflers grows algebraically with the population
size) at a finite value of the network parameter . A quantitative estimate
for the critical value of is obtained via extensive numerical simulations.Comment: 24 pages, 4 figure
A general Markov chain approach for disease and rumour spreading in complex networks
Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumour spreading are among the most important of these processes due to their practical relevance. However, despite the similarities between them, current models address both spreading dynamics separately. In this article, we propose a general spreading model that is based on discrete time Markov chains. The model includes all the transitions that are plausible for both a disease contagion process and rumour propagation. We show that our model not only covers the traditional spreading schemes but that it also contains some features relevant in social dynamics, such as apathy, forgetting, and lost/recovering of interest. The model is evaluated analytically to obtain the spreading thresholds and the early time dynamical behaviour for the contact and reactive processes in several scenarios. Comparison with Monte Carlo simulations shows that the Markov chain formalism is highly accurate while it excels in computational efficiency. We round off our work by showing how the proposed framework can be applied to the study of spreading processes occurring on social networks
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