A Stochastic Birth-Death Model of Information Propagation Within Human Networks

The fixation probability of a mutation in a population network is a widely-studied phenomenon in evolutionary dynamics. This mutation model following a Moran process finds a compelling application in modeling information propagation through human networks. Here we present a stochastic model for a two-state human population in which each of N individual nodes subscribes to one of two contrasting messages, or pieces of information. We use a mutation model to describe the spread of one of the two messages labeled the mutant, regulated by stochastic parameters such as talkativity and belief probability for an arbitrary fitness r of the mutant message. The fixation of mutant information is analyzed for an unstructured well-mixed population and simulated on a Barabási-Albert graph to mirror a human social network of \(N = 100\) individuals. Chiefly, we introduce the possibility of a single node speaking to multiple information recipients or listeners, each independent of one another, per a binomial distribution. We find that while in mixed populations, the fixation probability of the mutant message is strongly correlated with the talkativity (sample correlation \(\rho = 0.96\)) and belief probability (\(\rho = -0.74\)) of the initial mutant, these correlations with respect to talkativity (\(\rho = 0.61\)) and belief probability (\(\rho = -0.49\)) are weaker on BA graph simulations. This indicates the likely effect of added stochastic noise associated with the inherent construction of graphs and human networks.