The Role of Multiple Repetitions on the Size of a Rumor

Autor(es)

Rada, Alejandra ^[1] ; Coletti, Cristian ^[1] ; Lebensztayn, Elcio ^[2] ; Rodriguez, Pablo M. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 20, n. 3, p. 1209-1231, 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/22972-8 - Recorrência, entropia e aplicação em rumores.
• Beneficiário: Erika Alejandra Rada Mora
• Modalidade de apoio: Auxílio à Pesquisa - Regular