Critical behavior of the contact process on small-world networks

Abstract

We investigate the role of clustering on the critical behavior of the contact process (CP) on small-world networks using the Watts-Strogatz (WS) network model with an edge rewiring probability p. The critical point is well predicted by a homogeneous cluster-approximation for the limit of vanishing clustering (p close to 1). The critical exponents and dimensionless moment ratios of the CP are in agreement with those predicted by the mean-field theory for any p > 0. This independence on the network clustering shows that the small-world property is a sufficient condition for the mean-field theory to correctly predict the universality of the model. Moreover, we compare the CP dynamics on WS networks with rewiring probability p = 1 and random regular networks and show that the weak heterogeneity of the WS network slightly changes the critical point but does not alter other critical quantities of the model.

07 pages, 06 figures

References in corpus (7)

• Critical phenomena in complex networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Griffiths phases on complex networks
• Finite-size scaling in complex networks
• Langevin approach for the dynamics of the contact process on annealed scale-free networks
• Routes to thermodynamic limit on scale-free networks
• Quasi-stationary analysis of the contact process on annealed scale-free networks

Cited by in corpus (17)

• Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks
• Heterogeneous pair-approximation for the contact process on complex networks
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Collective versus hub activation of epidemic phases on networks
• Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks
• Metastable Localization of Diseases in Complex Networks
• Interacting opinion and disease dynamics in multiplex networks: discontinuous phase transition and non-monotonic consensus times
• Testing the critical brain hypothesis using a phenomelogical renormalization group
• Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks
• An overview of epidemic models with phase transitions to absorbing states running on top of complex networks
• Griffiths phases in infinite-dimensional, non-hierarchical modular networks
• High prevalence regimes in the pair quenched mean-field theory for the susceptible-infected-susceptible model on networks
• Simple quasistationary method for simulations of epidemic processes with localized states
• Multistage onset of epidemics in heterogeneous networks
• Bifurcations in synergistic epidemics on random regular graphs
• Dynamical correlations and pairwise theory for the symbiotic contact process on networks
• Competing contact processes in the Watts-Strogatz network