From subcritical behavior to elusive transitions in rumor models
arXiv:2102.11706 · doi:10.1038/s41467-022-30683-z
Abstract
Rumor and information spreading are natural processes that emerge from human-to-human interaction. Mathematically, this was explored in the popular Maki-Thompson model, where a phase transition was thought to be absent. Here, we show that a second-order phase transition is present in this model which is not captured by first-order mean-field approximations. Moreover, we propose and explore a modified version of the Maki-Thompson model that includes a forgetting mechanism. This modification changes the Markov chain's nature from infinitely many absorbing states in the classical setup to a single absorbing state. In practice, this allows us to use a plethora of analytic and numeric methods that permit the models' characterization. In particular, we find a counter-intuitive behavior in the subcritical regime of these models, where the lifespan of a rumor increases as the spreading rate drops, following a power-law relationship. This means that, even below the critical threshold, rumors can survive for a long time. Together, our findings suggest that the dynamic behavior of rumor models can be much richer than previously thought. Thus, we hope that our results motivate further research both analytically and numerically.
References in corpus (21)
- Epidemic processes in complex networks
- Dynamics of Rumor Spreading in Complex Networks
- Theory of Rumour Spreading in Complex Social Networks
- Generation of uncorrelated random scale-free networks
- Epidemic spreading in correlated complex networks
- Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
- Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
- Fundamentals of spreading processes in single and multilayer complex networks
- Modeling Rumors: The No Plane Pentagon French Hoax Case
- Contact processes on random graphs with power law degree distributions have critical value 0
- Non mean-field behavior of the contact process on scale-free networks
- Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks
- Nonequilibrium phase transitions and finite size scaling in weighted scale-free networks
- Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
- Collective versus hub activation of epidemic phases on networks
- Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks
- Steady-State Dynamics of the Forest Fire Model on Complex Networks
- Phase transition for the Maki-Thompson rumour model on a small-world network
- Skepticism and rumor spreading: the role of spatial correlations
- The lifespan method as a tool to study criticality in absorbing-state phase transitions
- Phase transitions with infinitely many absorbing states in complex networks