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Abstract: The dynamic behaviour of stochastic spreading processes on a network modelbased on k-regular graphs is investigated. The contact process and thesusceptible-infected-susceptible model for the spread of epidemics areconsidered as prototype stochastic spreading processes. We study these on anetwork consisting of a mixture of 2- and 3-fold oordinated randomly-connectednodes 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=12-regular graph - 1D chain allows us to investigate their behaviour undersuch structural changes. Both processes are expected to exhibit mean-fieldfeatures for p=0 and features typical of the directed percolation universalityclass for p=1. The analysis is undertaken by means of Monte Carlo simulationsand the application of mean-field theory. The quasi-stationary simulationmethod is used to obtain the phase diagram for the processes in thisenvironment along with critical exponents. Predictions for critical exponentsobtained from mean-field theory are found to agree with simulation results overa large range of values for p up to a value of p=0.95, where the system isfound to sharply cross over to the one-dimensional case. Estimates of criticalthresholds given by mean-field theory are found to underestimate thecorresponding critical rates obtained numerically for all values of p.



Author: S. V. Fallert, S. N. Taraskin

Source: https://arxiv.org/



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