Stochastic spreading processes on a network model based on regular graphs

Abstract

The dynamic behaviour of stochastic spreading processes on a network model based on k-regular graphs is investigated. The contact process and the susceptible-infected-susceptible model for the spread of epidemics are considered as prototype stochastic spreading processes. We study these on a network consisting of a mixture of 2- and 3-fold oordinated randomly-connected nodes of concentration p and 1-p, respectively, with p varying between 0 and 1. Varying the parameter p from p=0 (3-regular graph of infinite dimension) to p=1 (2-regular graph - 1D chain) allows us to investigate their behaviour under such structural changes. Both processes are expected to exhibit mean-field features for p=0 and features typical of the directed percolation universality class for p=1. The analysis is undertaken by means of Monte Carlo simulations and the application of mean-field theory. The quasi-stationary simulation method is used to obtain the phase diagram for the processes in this environment along with critical exponents. Predictions for critical exponents obtained from mean-field theory are found to agree with simulation results over a large range of values for p up to a value of p=0.95, where the system is found to sharply cross over to the one-dimensional case. Estimates of critical thresholds given by mean-field theory are found to underestimate the corresponding critical rates obtained numerically for all values of p.

to be published in Springer Lecture Notes in Computer Science

References in corpus (10)

• Statistical mechanics of complex networks
• Epidemic spreading in scale-free networks
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Epidemic dynamics and endemic states in complex networks
• Absence of epidemic threshold in scale-free networks with connectivity correlations
• Spectra of complex networks
• Finite-size scaling in complex networks
• Universal finite-size scaling behavior and universal dynamical scaling behavior of absorbing phase transitions with a conserved field
• Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation
• Finite-size scaling of directed percolation above the upper critical dimension