论文标题
多次重复在谣言大小上的作用
The role of multiple repetitions on the size of a rumor
论文作者
论文摘要
我们提出了一个数学模型，以衡量在给定暴发期间从未听到过谣言的最终人群中多次重复的影响。该模型是一种多维连续时间马尔可夫链，可以看作是Maki-Thompson模型的概括，用于在同质混合种群中传播谣言。在众所周知的基本模型中，人口由“撒布者”，“无知者”和“僵硬者”组成，任何吊具都试图通过定向联系将谣言传播给其他人。如果接触的个人是一个无知的人，它将成为撒布机，而在其他两种情况下，启动散布器会变成僵硬的人。有限人口中的过程最终将达到平衡状况，个人是僵硬者或无知者。我们通过假设每个无知者才能在听到谣言的预定次数之后才能成为一个散布器来概括该模型。我们识别和分析模型的合适限制动力学系统，并证明限制了表征不同人群不同类别中个体最终比例的定理。
We propose a mathematical model to measure how multiple repetitions may influence in the ultimate proportion of the population never hearing a rumor during a given outbreak. The model is a multi-dimensional 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.
