On Rumour Propagation Among Sceptics

On the probability of rumour survival among sceptics

“…However, our novelties are related to the extension of the rumour process to the sceptical one and its mathematical modelling, and especially to the construction of a convenient discrete-time renewal process, which is difficult to define due to the complexity of our model. We also prove that the condition for the rumour process to survive among the sceptics is equivalent to the available condition of surviving among the non-sceptics, which is in line with the results in [9] and [23].…”

“…Our model may be seen to be equivalent to this formulation by taking and to have the same distribution as that of , where is a generic random variable with the same distribution as . Therefore Theorem 3 says that under our setup for the propagation model and also under the setup in [23], we have the same result for the probability that the rumour survives among the sceptics.…”

“…Our model for the investigation of sceptical rumour spread is different from those of [9] and [23], and is an extension of the classical model in [10] such that the information transfers more slowly in our model. Similarly to the previous versions of information transmission, the probability of survival is the first issue.…”

“…It should be noted that related results were first obtained by Athreya et al [1] in the context of space covering processes. For more recent work on this model, see [3], [10], [16], and [23]. In 2014, Gallo et al [10] found necessary and sufficient conditions for survival of the rumour.…”

“…Rumour propagation among sceptics was first introduced by Sajadi and Roy [23]. They introduced sceptics: the individuals who need to receive the rumour from at least two different sources to accept and transmit it.…”