Title: Going Viral: Stability of Consensus-Driven Adoptive Spread,
Abstract: The spread of new products in a networked population is often modeled as an
epidemic. However, in the case of "complex" contagion, these models are
insufficient to properly model 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. To conclude, numerical simulations demonstrate behavior
of the model which reflect findings from the sociology literature on adoption
behavior.