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Threshold based models have been widely used in characterizing collectivebehavior on social networks. An individual's threshold indicates the minimumlevel of influence that must be exerted, by other members of the populationengaged in some activity, before the individual will join the activity. In thiswork, we begin with a homogeneous version of the Linear Threshold modelproposed by Kempe et al. in the context of viral marketing, and generalize thismodel to arbitrary threshold distributions. We show that the evolution can bemodeled as a discrete time Markov chain, and, by using a certain scaling, weobtain a fluid limit that provides an ordinary differential equation model(o.d.e.). We find that the threshold distribution appears in the o.d.e. via itshazard rate function. We demonstrate the accuracy of the o.d.e. approximationand derive explicit expressions for the trajectory of influence under theuniform threshold distribution. Also, for an exponentially distributedthreshold, we show that the fluid dynamics are equivalent to the well-known SIRmodel in epidemiology. We also numerically study how other hazard functions(obtained from the Weibull and loglogistic distributions) provide qualitativedifferent characteristics of the influence evolution, compared to traditionalepidemic models, even in a homogeneous setting. We finally show how the modelcan be extended to a setting with multiple communities and conclude withpossible future directions.

Influence Spread in Social Networks: A Study via a Fluid Limit of the Linear Threshold Model