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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The Role of Multiple Repetitions on the Size of a Rumor

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Author(s):
Rada, Alejandra [1] ; Coletti, Cristian [1] ; Lebensztayn, Elcio [2] ; Rodriguez, Pablo M. [3]
Total Authors: 4
Affiliation:
[1] Univ Fed Abc, Ctr Matemat Comp & Cognicao, 5001 Bangu, Santo Andre, SP - Brazil
[2] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, BR-13083859 Campinas, SP - Brazil
[3] Univ Fed Pernambuco, Ctr Ciencias Exatas & Nat, BR-50670901 Recife, PE - Brazil
Total Affiliations: 3
Document type: Journal article
Source: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 20, n. 3, p. 1209-1231, 2021.
Web of Science Citations: 0
Abstract

We propose a mathematical model to measure how multiple repetitions may influence the ultimate proportion of the population never hearing a rumor during a given outbreak. The model is a multidimensional continuous-time Markov chain that can be seen as a generalization of the Maki-Thompson model for the propagation of a rumor within a homogeneously mixing population. In the well-known basic model, the population is made up of ``spreaders,{''} ``ignorants,{''} and ``stiflers,{''} and any spreader attempts to transmit the rumor to the other individuals via directed contacts. In case the contacted individual is an ignorant, it becomes a spreader, while in the other two cases the initiating spreader turns into a stifler. The process in a finite population will eventually reach an equilibrium situation, where individuals are either stiflers or ignorants. We generalize the model by assuming that each ignorant becomes a spreader only after hearing the rumor a predetermined number of times. We identify and analyze a suitable limiting dynamical system of the model, and we prove limit theorems that characterize the ultimate proportion of individuals in the different classes of the population. (AU)

FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/22972-8 - Recurrence, entropy and application in rumors.
Grantee:Erika Alejandra Rada Mora
Support Opportunities: Regular Research Grants