Discontinuous Transition of a Multistage Independent Cascade Model on Networks

Abstract

We propose a multistage version of the independent cascade model, which we call a multistage independent cascade (MIC) model, on networks. This model is parameterized by two probabilities: the probability $T_1$ that a node adopting a fad increases the awareness of a neighboring susceptible node, and the probability $T_2$ that an adopter directly causes a susceptible node to adopt the fad. We formulate a tree approximation for the MIC model on an uncorrelated network with an arbitrary degree distribution $p_k$. Applied on a random regular network with degree $k=6$, this model exhibits a rich phase diagram, including continuous and discontinuous transition lines for fad percolation, and a continuous transition line for the percolation of susceptible nodes. In particular, the percolation transition of fads is discontinuous (continuous) when $T_1$ is larger (smaller) than a certain value. A similar discontinuous transition is also observed in random graphs and scale-free networks. Furthermore, assigning a finite fraction of initial adopters dramatically changes the phase boundaries.

15 pages, 11 figures

References in corpus (9)

• Threshold effects for two pathogens spreading on a network
• Predicting the size and probability of epidemics in a population with heterogeneous infectiousness and susceptibility
• Multi-Stage Complex Contagions
• On the critical behavior of the Susceptible-Infected-Recovered (SIR) model on a square lattice
• Reinforcement-Driven Spread of Innovations and Fads
• Ordering dynamics of the multi-state voter model
• The Role of Second Trials in Cascades of Information over Networks
• Transition-type change between an inverted Berezinskii-Kosterlitz-Thouless transition and an abrupt transition in the bond percolation on a random hierarchical small-world network
• Outbreak size distributions in epidemics with multiple stages

Cited by in corpus (7)

• Universal mechanism for hybrid percolation transitions
• Outbreaks in susceptible-infected-removed epidemics with multiple seeds
• Mixed-order phase transition in a two-step contagion model with single infectious seed
• Critical behavior of a two-step contagion model with multiple seeds
• Sudden spreading of infections in an epidemic model with a finite seed fraction
• Two golden times in two-step contagion models
• The dynamics of two-stage contagion