多次重复对谣言大小的作用
The role of multiple repetitions on the size of a rumor
摘要：
我们提出了一个数学模型，以衡量如何多次重复可能会影响在最终比例的人口从来没有听到谣言在一个给定的爆发。该模型是一个多维连续时间的马尔可夫链，可以看作是一个推广的Maki-Thompson模型的谣言传播均匀混合人口。在著名的基本模型中，种群由“传播者”、“传播者”和“扼杀者”组成，任何传播者都试图通过直接接触将谣言传播给其他个体。如果接触的个人是无知的，它就变成了传播者，而在其他两种情况下，发起传播者变成了扼杀者。在一个有限总体中，这个过程最终会达到一个平衡状态，在这个平衡状态中，个体要么是stifler，要么是benefants。我们通过假设每个无知者只有在听到谣言预定次数后才成为传播者来推广模型。我们确定并分析了一个合适的限制动力系统的模型，我们证明了极限定理，其特征在于最终的比例的个人在不同类别的人口。
英文摘要：
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.
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