Critical properties of contact process on the Apollonian network

We investigate an epidemic spreading process by means of a computational simulation on the Apollonian network, which is simultaneously small-world, scale-free, Euclidean, space-filling and matching graphs. An analysis of the critical behavior of the Contact Process (CP) is presented using a Monte Carlo method. Our model shows a competition between healthy and infected individuals in a given biological or technological system, leading to a continuous phase transition between the active and inactive states, whose critical exponents β/_ν⊥$\beta /{\nu }_{\perp }$ and 1/_ν⊥$1/{\nu }_{\perp }$ are calculated. Employing a finite-size scaling analysis, we show that the continuous phase transition belongs to the mean-field directed percolation universality class in regular lattices.