Ferraz de Arruda Guilherme, Jeub Lucas G S, Mata Angélica S, Rodrigues Francisco A, Moreno Yamir
ISI Foundation, Via Chisola 5, 10126, Torino, Italy.
Departamento de Física, Universidade Federal de Lavras, 37200-900, Lavras, Minas Gerais, Brazil.
Nat Commun. 2022 Jun 1;13(1):3049. doi: 10.1038/s41467-022-30683-z.
Rumors and information spreading emerge naturally from human-to-human interactions and have a growing impact on our everyday life due to increasing and faster access to information, whether trustworthy or not. A popular mathematical model for spreading rumors, data, or news is the Maki-Thompson model. Mean-field approximations suggested that this model does not have a phase transition, with rumors always reaching a fraction of the population. Conversely, here, we show that a continuous phase transition is present in this model. Moreover, we explore a modified version of the Maki-Thompson model that includes a forgetting mechanism, changing the Markov chain's nature and allowing us to use a plethora of analytic and numeric methods. Particularly, we characterize the subcritical behavior, where the lifespan of a rumor increases as the spreading rate drops, following a power-law relationship. Our findings show that the dynamic behavior of rumor models is much richer than shown in previous investigations.
谣言和信息传播自然地产生于人际互动之中，并且由于获取信息（无论是否可靠）的途径越来越多、速度越来越快，它们对我们的日常生活产生着越来越大的影响。一种用于传播谣言、数据或新闻的流行数学模型是牧木-汤普森模型。平均场近似表明该模型不存在相变，谣言总是会传播到一定比例的人群。相反，在这里我们表明该模型存在连续相变。此外，我们探索了牧木-汤普森模型的一个修改版本，该版本包含遗忘机制，改变了马尔可夫链的性质，并使我们能够使用大量的解析和数值方法。特别地，我们刻画了亚临界行为，即随着传播速率下降，谣言的寿命会按照幂律关系增加。我们的研究结果表明，谣言模型的动态行为比以往研究所显示的要丰富得多。
