The stochastic evolution of rumors within a population

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• 作者：Muhammad Zaid Dauhoo ; ^{m.dauhoo@uom.ac.mu" class="auth_mail" title="E-mail the corresponding author} ; Diksha Juggurnath ; Noure-Roukayya Badurally Adam
• 刊名：Mathematical Social Sciences
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：82
• 期：Complete
• 页码：85-96
• 全文大小：1128 K

文摘

We study rumor propagation process with incubation and constant immigration. We take into account a deterministic rumor spreading model and demonstrate the persistence of a rumor when the basic reproduction number is greater than one. Due to the presence of a randomness in the influence that the incubators exert on ignorants, we extrapolate the deterministic rumor model to a stochastic one by using a stochastic coefficient for the term representing the latter influence within the system. The existence and boundedness of both local and global solutions are demonstrated. We prove the uniqueness of these solutions. Conditions of extinction is also established. We perform numerical simulations to verify our stochastic model. The present work can assist decision takers in the analysis of the dynamical evolution of rumors in a given society as well as in the study of information dissemination strategies.