The spread of new products in a networked population is often modeled as an epidemic. However, in the case of “complex” contagion, these models do not capture nuanced, dynamic social reinforcement effects in adoption behavior. In this paper, we investigate a model of complex contagion which allows a coevolutionary interplay between adoption, modeled as an SIS epidemic spreading process, and social reinforcement effects, modeled as consensus opinion dynamics. Asymptotic stability analysis of the all-adopt as well as the none-adopt equilibria of the combined opinion-adoption model is provided through the use of Lyapunov arguments. In doing so, sufficient conditions are provided which determine the stability of the “flop” state, where no one adopts the product and everyone's opinion of the product is least favorable, and the “hit” state, where everyone adopts and their opinions are most favorable. These conditions are shown to extend to the bounded confidence opinion dynamic under a stronger assumption on the model parameters. Additional analysis is provided for the case where the product is neither a hit nor a flop. To conclude, numerical simulations demonstrate behaviors indicated in the sociology literature such as tipping points.

中文翻译：

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病毒式传播：共识驱动的采用传播的稳定性

新产品在网络人群中的传播通常被建模为流行病。然而，在“复杂”传染的情况下，这些模型没有捕捉到收养行为中细微的、动态的社会强化效应。在本文中，我们研究了一种复杂传染模型，该模型允许采用（以 SIS 流行病传播过程为模型）和社会强化效应（以共识意见动态为模型）之间的协同进化相互作用。通过使用李雅普诺夫论证，提供了对组合意见采用模型的全采用和非采用均衡的渐近稳定性分析。这样做，提供了确定“翻牌”状态稳定的充分条件，即没有人采用产品，每个人对产品的看法都最差，“命中”状态，每个人都采用并且他们的意见最有利的地方。在对模型参数的更强假设下，这些条件被证明可以扩展到有界置信意见动态。为产品既不是热门产品也不是失败产品的情况提供了额外的分析。总而言之，数值模拟展示了社会学文献中指出的行为，例如临界点。